%% %%% example thesis bib file %%% %%% %%% Books appear first in the list. Inproceedings next, %%% then articles, unpublished appears last. %%% Each section appears in alphabetical order. %%% To skip to the r-section of books (for example), search for: %%% book-r %%% %%% %%% Tags or the citation label have a very simple system here %%% if: %%% author = R. L. Devaney %%% title = An Introduction to Chaotic Dynamical %%% Systems %%% year = 1986 %%% then: %%% tag = devaney:icd86 %%% %%% use all lowercase!! %%% last-name-first-author:first-three-significant-word-initials_year %%% %%% (read some examples below before adding to this database) %%% %%% If you are using a local (Utah) version of emacs, then some %%% bindings are set up for the formatting. For a complete list %%% type c-h m %%% Example: C-c C-e C-b bibtex-Book %%% C-c C-e C-a bibtex-Article %%% C-c C-e C-u bibtex-Unpublished %%% %%% %%% FOR YOUR SANITY: KEEP IN ALPHABETICAL ORDER %%% %%% %%% defns %%% @String{ACPR = "Academic Press"} @String{AP = "Acta Physica"} @String{AdvAplMath = "Advances in Applied Mathematics"} @String{ARCH = "Arch. Rat. Mech. Anal."} @String{BAMS = "Bulletin of the AMS"} @String{BIOPJ = "Biophys. Jour."} @String{BMB = "Bull. Math. Biol."} @String{Bfz = "Biofizika"} @String{Bph = "Biophysics"} @String{CoCh = "J. of Comp. Chem."} @String{CMP = "Communications on Mathematical Physics"} @String{DIE = "Diff. Int. Eqns."} @String{JDE = "J. Diff. Eqns."} @String{JMB = "J. Math. Biol."} @String{JTB = "J. Theor. Biol."} @String{JSTP = "J. Stat. Phys."} @String{LNM = "Lecture Notes in Mathematics"} @String{LNBM = "Lecture Notes in Biomathematics"} @String{MGHILL = "McGraw-Hill"} @String{NAT = "Nature"} @String{PHYD = "Physica D"} @String{PHYLA = "Phys. Rev. Letts. A"} @String{PHYsrevlet = "Phys. Rev. Letts. A"} @String{ProgTPhys = "Prog. of Theor. Phys"} @String{SCI = "Science"} @String{SJAM = "SIAM J. Appl. Math."} @String{SJSS = "SIAM J. Sci. Stat. Comput."} @String{Srev = "SIAM Rev."} @String{SPR = "Springer-Verlag"} @String{TChem = "Theoretical Chemistry"} @String{WILEY = "John Wiley and Sons"} %%% %%% Publishers %%% @String{pub-AHV = "Dr. Alfred H{\"u}thing Verlag"} @String{pub-AHV:adr = "Heidelberg, Germany"} @String{pub-AMS = "American Mathematical Society"} @String{pub-AP = "Academic Press"} @String{pub-ASCII = "ASCII Corporation"} @String{pub-AW = "Ad{\-d}i{\-s}on-Wes{\-l}ey"} @String{pub-AW:adr = "Reading, MA, USA"} @String{pub-AWE = "Ad{\-}di{\-}son-Wes{\-}ley Europe"} @String{pub-AWE:adr = "Amsterdam, The Netherlands"} @String{pub-AWV = "Ad{\-}di{\-}son-Wes{\-}ley Verlag"} @String{pub-AWV:adr = "Bonn, Germany"} @String{pub-BOWK = "R. R. Bowker Company"} @String{pub-BOWK:adr = "1180 Avenue of the Americas, New York, NY 10036, USA"} @String{pub-BP = "Boole Press"} @String{pub-BP:adr = "Dublin, Ireland"} @String{pub-CHARTWELL = "Chartwell Books, Inc."} @String{pub-CHARTWELL:adr = "110 Enterprise Avenue, Secaucus, New Jersey 07094, USA"} @String{pub-CIAOCO = "Editions Ciaoco"} @String{pub-CIAOCO:adr = "Artel, Bruxelles, Belgium"} @String{pub-CUP = "Cambridge University Press"} @String{pub-CUP:adr = "New York"} @String{pub-DP = "Digital Press"} @String{pub-EH = "Ellis Horwood"} @String{pub-EH:adr = "Chichester, England"} @String{pub-EUH = "Editore Ulrico Hoepli"} @String{pub-EUH:adr = "Ulrico Hoepli Editore S.p.A., via Hoepli 5, 20121 Milano, Italy"} @String{pub-FCGCC = "F{\'e}d{\'e}ration C. G. C. de la Communication"} @String{pub-FCGCC:adr = ""} @String{pub-GP = "Graphics Press"} @String{pub-GP:adr = "Box 430, Cheshire, CT 06410, USA"} @String{pub-IE = "InterEditions"} @String{pub-IST = "Imaging Science \& Technology"} @String{pub-KLUWER = "Kluwer Academic Publishers Group"} @String{pub-KLUWER:adr = "Norwell, MA, USA"} @String{pub-MH = "McGraw-Hill"} @String{pub-MASSON = "Masson Editeur"} @String{pub-MASSON:adr = "Paris, France"} @String{pub-MIT = "MIT Press"} @String{pub-MIT:adr = "Cambridge, MA, USA"} @String{pub-NH = "North-Holland Publishing Company"} @String{proc-NIPT91 = "IS\&T's Seventh International Congress on Advances in Non-impact Printing Technologies, October 6--11, Portland, OR, USA."} @String{pub-PEACHPIT = "Peachpit Press, Inc."} @String{pub-PEACHPIT:adr = "1085 Keith Avenue, Berkeley, CA 94708, USA"} @String{pub-PTI = "Personal {\TeX} Inc."} @String{pub-PTI:adr = "12 Madrona Street, Mill Valley, CA 94941, USA"} @String{pub-OLDENBOURG = "R. Oldenbourg Verlag"} @String{pub-OLDENBOURG:adr = "Munich, Germany and Vienna, Austria"} @String{pub-RISO = "Ris{\o} National Laboratory"} @String{pub-RISO:adr = "Roskilde, Denmark"} @String{pub-SF = "Scott, Foresman and Company"} @String{pub-SILICON = "Silicon Press"} @String{pub-SILICON:adr = "25 Beverly Road, Summit, NJ 07901, USA"} @String{pub-STA = "Society of Typographic Arts"} @String{pub-STA:adr = "Chicago, IL, USA"} @String{pub-SV = "Spring{\-}er-Ver{\-}lag"} @String{pub-SV:adr = "Berlin, Germany~/ Heidelberg, Germany~/ London, England~/ etc."} @String{pub-SYBEX = "Sybex"} @String{pub-TEXPLORATOR = "The {\TeX}plorators Corporation"} @String{pub-TEXPLORATOR:adr = "3701 W. Alabama, Suite 450-273, Houston, TX 77027, USA"} @String{pub-UNIC = "UNI{$\bullet$}C"} @String{pub-UNIC:adr = "Danmarks EDB-Center for Forskning og Uddannelse, Copenhagen, Denmark"} @String{pub-URW = "URW Verlag"} @String{pub-URW:adr = "Hamburg, Germany"} @String{pub-VNR = "Van Nostrand Reinhold"} @String{pub-W = "Wiley"} @String{pub-WGP = "Wat{\-}son-Gup{\-}till Publications"} @String{pub-WWS = "The Wynkyn de Worde Society and Bund Deutscher Buchk{\"u}nstler"} @String{pub-WWS:adr = "London, England and Offenbach, Germany"} %%% %%% books 90 volumes as of [Jan- 9-1993] %%% % % book-a % @Book{adams:ss75, author = "R. Adams", title = "Sobolev {S}paces", publisher = "Academic Press", year = "1975", address = "New York", } @Book{allgower:ncm90, author = "E. L. Allgower and K. Georg", title = "Numerical Continuation Methods, An Introduction", publisher = "Springer-Verlag", year = "1990", address = "New York", annote = "bifurcation", } @Book{amann:gd83, author = "H. Amann", title = "Ordinary {D}ifferential {E}quations", publisher = "de Gruyter", year = "1990", address = "Berlin", annote = "", } @Book{ambrosetti:anl73, author = "A. Ambrosetti and G. Prodi", title = "Analisis {N}on {L}ineare", publisher = "Scuola Normale Superiore Pisa", year = "1973", annote = "BIF", } @Book{arnold:gmt83, author = "V. I. Arnold", title = "Geometrical {M}ethods in the {T}heory of {O}rdinary {D}ifferential {E}quations", publisher = "Springer-Verlag", year = "1983", address = "New York", annote = "ode", } % % book-b % @Book{bandle:iia80, author = "C. Bandle", title = "Isoperimetric {I}nequalities and {A}pplications", publisher = "Pitman", year = "1980", address = "London", annote = "PDE", } @Book{bebernes:mpc89, author = "J. Bebernes and D. Eberly", title = "Mathematical {P}roblems from {C}ombustion {T}heory", publisher = "Springer Verlag", year = "1989", volume = "83", address = "New York", series = "Applied Math. Sci.", annote = "PDE", } @Book{berger:nfa77, author = "M. S. Berger", title = "Nonlinearity and {F}unctional {A}nalysis", publisher = "Academic Press", address = "New York", year = "1977", annote = "BIF", } @Book{berger:pn68, author = "M. S. Berger and M. S. Berger", title = "Perspectives in {N}onlinearity", publisher = "Benjamin", address = "", year = "1968", annote = "BIF", } % % book-c % @Book{carr:acm81, author = "J. Carr", title = "Applications of {C}entre {M}anifold {T}heory", publisher = "Springer Verlag", year = "1981", address = "New York", annote = "BIF", } @Book{chandrasekhar:iss57, author = "S. Chandrasekhar", title = "An Introduction to the Study of Stellar Structures", publisher = "Dover", year = "1957", address = "Chicago", annote = "stellar equilibrium", } @Book{chow:mbt82, author = "S. N. Chow and J. K. Hale", title = "Methods of {B}ifurcation {T}heory", publisher = "Springer Verlag", year = "1982", address = "Berlin", annote = "BIF", } @Book{collett:imi80, author = "J. P. Collett and J. P. Eckmann", title = "Iterated maps of the interval as dynamical systems", publisher = "Birkhauser-Verlag", year = "1980", address = "Boston", annote = "1D maps", } % % book-d % @Book{davis:ind62, author = "H. Davis", title = "Introduction to {N}onlinear {D}ifferential and {I}ntegral {E}quations", publisher = "Dover", year = "1962", address = "New York", annote = "Emden equation", } @Book{deimling:nga74, author = "K. Deimling", title = "Nichtlineare Gleichungen und Abbildungsgrade", publisher = "Springer Verlag", year = "1974", address = "Berlin", } @Book{deimling:nfa87, author = "K. Deimling", title = "Nonlinear {F}unctional {A}nalysis", publisher = "Springer Verlag", year = "1987", address = "New York", annote = "BIF", } @Book{dennis:mmu83, author = "J. Dennis and R. Schnabel", title = "Numerical {M}ethods for {U}nconstrained {O}ptimization and {N}onlinear {E}quations", publisher = "Prentice-Hall", year = "1983", address = "Englewood Cliffs, N.J.", annote = "newtons's method", } @Book{devaney:icd86, author = "R. L. Devaney", title = "An {I}ntroduction to {C}haotic {D}ynamical {S}ystems", publisher = "Benjamin-Cummings", year = "1986", } @Book{dieudonne:fma64, author = "J. Dieudonn{\'e}", title = "Foundations of Modern Analysis", publisher = "Academic Press", year = "1964", address = "New York", annote = "Analysis", } @Book{doedel:obp87a, author = "E. J. Doedel and J. P. Kern\'evez", title = "Optimization in bifurcation problems, Part~{I} : Theory and illustration", publisher = "Springer Verlag", year = "1987", series = "Lecture Notes in Control and Information Sciences", address = "New York", note = "in press", annote = "bifurcation, numerical analysis", } @Book{doedel:obp87b, author = "E. J. Doedel and J. P. Kern\'evez", title = "Optimization in bifurcation problems, Part~{II} : Numerical method and applications", publisher = "Springer Verlag", year = "1987", series = "Lecture Notes in Control and Information Sciences", address = "New York", note = "in press", annote = "bifurcation", } @Book{dongarra:sls91, author = "J. Dongarra and I. Duff and D. Sorensen and H. van der Vorst", title = "Solving Linear Systems on Vector and Shared Memory Computers", publisher = "SIAM", year = "1991", address = "Philadelphia", annote = "parallel", } @Book{dugundji:t73, author = "J. Dugundji", title = "Topology", publisher = "Allyn and Bacon", year = "1973", address = "Boston", annote = "Topology", } % % book-f % @Book{fife:mar79, author = "P. Fife", title = "Mathematical Aspects of Reacting and Diffusing Systems", publisher = "Springer Verlag", year = "1979", volume = "28", series = "Springer Lecture Notes in Biomathematics", address = "Berlin", annote = "PDE", } @Book{fink:apd74, author = "A. M. Fink", title = "Almost Periodic Differential Equations", publisher = "Springer Verlag", year = "1974", volume = "377", address = "Berlin", annote = "DE" } @Book{frank:dhe55, author = "D. A. Frank-Kamanetski", title = "Diffusion and Heat Exchange in Chemical Kinetics", publisher = "Princeton University Press", year = "1955", address = "Princeton", annote = "Gelfand example", } @Book{fucik:sne81, author = "S. Fucik", title = "Solvability of Nonlinear Equations and Boundary Value problems", publisher = "Reidel", year = "1981", address = "Boston", annote = "PDE", } @Book{fucik:san73, author = "S. Fucik and J. Necas and V. Soucets", title = "Spectral {A}nalysis of {N}onlinear {O}perators", publisher = "Springer Verlag", year = "1973", volume = "343", series = "Lecture Notes in Math", address = "Berlin", annote = "BIF", } % % book-g % @Book{gaines:cdn77, author = "R. Gaines and J. Mawhin", title = "Coincidence Degree and Nonlinear Differential Equations", publisher = "Springer Verlag", year = "1977", volume = "568", series = "Springer Lecture Notes in Math", address = "Berlin", annote = "degree", } @Book{gilbarg:epd83, author = "D. Gilbarg and N. Trudinger", title = "Elliptic Partial Differential Equations of Second Order", publisher = "Springer Verlag", year = "1983", address = "Berlin", annote = "PDE", } @Book{golub:mc89, author = "G. Golub and C. van Loan", title = "Matrix Computations", publisher = "Johns Hopkins Univ. Press", year = "1989", address = "Baltimore", annote = "numerical linear algebra", } @Book{guckenheimer:nod83, author = "J. Guckenheimer and P. Holmes", title = "Nonlinear {O}scillations, {D}ynamical {S}ystems and {B}ifurcations of {V}ector {F}ields", publisher = "Springer Verlag", year = "1983", volume = "42", series = "Applied Mathematical Sciences", institution = "SPR", address = "New York", annote = "BIF", } % % book-h % @Book{hahn:sm67, author = "W. Hahn", title = "Stability of Motion", publisher = "Springer Verlag", year = "1967", address = "Berlin", annote = "Stability", } @Book{hale:tdb80, author = "J. Hale", title = "Topics in dynamic bifurcation theory", publisher = "AMS", year = "1980", annote = "bifurcation theory", } @Book{hale:tfd67, author = "J. Hale", title = "Theory of Functional Differential Equations", publisher = "Springer Verlag", year = "1977", address = "Berlin", annote = "FDE", } @Book{hartman:ode82, author = "P. Hartman", title = "Ordinary Differential Equations", publisher = "Birkhauser", year = "1982", address = "Boston", edition = "second~ed.", annote = "ODE", } @Book{hassard:tah81, author = "B. D. Hassard and N. D. Kazarinoff and Y.-H. Wan", title = "Theory and Applications of Hopf Bifurcation", publisher = "Cambridge University Press", year = "1981", address = "Cambridge", annote = "Hopf bifurcation", } @Book{hirsch:ded74, author = "M. Hirsch and S. Smale", title = "Differential Equations, Dynamical Systems and Linear Algebra", publisher = "Academic Press", year = "1974", address = "New York", annote = "ODE" } @Book{holmes:nan80, author = "P. Holmes", title = "New approaches to nonlinear problems in dynamics", publisher = "SIAM", year = "1980", annote = "bifurcation", } @Book{horn:ma85, author = "R.A. Horn and C.R. Johnson", title = "Matrix {A}nalysis", publisher = "Cambridge University Press", year = "1985", address = "New York", annote = "numerical" } % % book-i % @Book{iooss:esb80, author = "G. Iooss and D. D. Joseph", title = "Elementary {S}tability and {B}ifurcation {T}heory", publisher = "Springer Verlag", year = "1980", address = "New York", annote = "BIF", } @Book{ize:btf76, author = "J. Ize", title = "Bifurcation {T}heory for {F}redholm {O}perators", publisher = "Memoires AMS", year = "1976", volume = "174", annote = "BIF", } % % book-j % @Book{jeggle:nf79, author = "H. Jeggle", title = "Nichtlineare {F}unktionalanalysis", publisher = "Teubner", year = "1979", annote = "BIF", } @Book{john:pws55, author = "F. John", title = "Plane {W}aves and {S}herical {M}eans Applied to {P}artial {D}ifferential {E}quations", publisher = "Interscience", year = "1955", volume = "2", series = "Tracts in Pure and Applied Mathematics", address = "New York", annote = "PDE", } @Book{john:pde82, author = "F. John", title = "Partial Differential Equations", publisher = "Springer-Verlag", year = "1982", volume = "1", series = "Applied Mathematical Sciences", address = "New York", annote = "PDE", } % % book-k % @Book{kato:ptl66, author = "T. Kato", title = "Perturbation {T}heory for {L}inear {O}perators", publisher = "Springer Verlag", year = "1966", address = "Berlin", annote = "BIF", } @Book{kawohl:rcl85, author = "B. Kawohl", title = "Rearrangements and {C}onvexity of {L}evel {S}ets in {PDE}", publisher = "Springer Verlag", year = "1985", volume = "1150", series = "Lecture Notes in Math.", address = "Berlin", annote = "PDE", } @Book{keller:btn69, author = "J. B. Keller and S. Antmaun", title = "Bifurcation {T}heory and {N}onlinear {E}igenvalue {P}roblems", publisher = "Benjamin", year = "1969", annote = "BIF", } @Book{kellog:fpt53, author = "O. D. Kellog", title = "Foundations of Potential Theory", publisher = "Dover", year = "1953", annote = "PDE", } @Book{kesavan:tfa89, author = "S. Kesavan", title = "Topics in Functional Analysis and Applications", publisher = "Wiley Eastern", year = "1989", address = "New Deli, India", annote = "PDE", } @Book{krasnoselskii:tmt64, author = "M. A. Krasnosel'skii", title = "Topological {M}ethods in the {T}heory of {N}onlinear {I}ntegral {E}quations", publisher = "Pergamon", year = "1964", annote = "BIF", } @Book{krasnoselskii:pso64, author = "M. A. Krasnosel'skii", title = "Positive {S}olutions of {O}perator {E}quations", publisher = "Noordhoff", year = "1964", address = "Groningen", annote = "BIF", } @Book{krasnoselskii:gmn84, author = "M. Krasnosel'skii and P. Zabreiko", title = "Geometrical Methods of Nonlinear Analysis", publisher = "Springer", year = "1984", address = "Berlin", annote = "Nonlinear Analysis", } @Book{krasnoselskii:ott68, author = "M. Krasnosel'skii", title = "The Operator of Translation Along Trajectories of Ordinary Differential Equations", publisher = "AMS", year = "1968", address = "Providence", annote = "ODE", } @Book{kubicek:cmb83, author = "M. Kubicek and M. Marek", title = "Computational methods in bifurcation theory and dissipative structures", publisher = "Springer Verlag", year = "1983", address = "New York", annote = "bifurcation, numerical analysis", } % % book-l % @Book{ladyzhenskaya:lqe68, author = "O. A. Ladyzhenskaya and N. N. Ural'tseva", title = "Linear and {Q}uasilinear {E}lliptic {E}quations", publisher = "Academic Press", year = "1968", volume = "46", series = "Math. in Sci. and Eng.", address = "New York", annote = "PDE", } @Book{ladyzhenskaya:bvp85, author = "O. A. Ladyzhenskaya", title = "The Boundary Value Problems of Mathematical Physics", publisher = "Springer Verlag", year = "1985", volume = "49", series = "App. Math. Sci.", annote = "PDE", } @Book{lloyd:dt78, author = "N. Lloyd", title = "Degree Theory", publisher = "Cambridge Univ. Press", year = "1978", address = "Cambridge", annote = "degree", } @Book{luenberger:iln73, author = "D. G. Luenberger", title = "Introduction to {L}inear and {N}onlinear {P}rogramming", publisher = "Addison-Wesley", year = "1973", address = "New York", annote = "numerics", } % % book-m % @PhdThesis{mcgough:scq93, author = "J. S. Mc{G}ough", title = "On {S}olution {C}ontinua in {Q}uasilinear {E}lliptic {P}roblems", school = "University of Utah", year = "1993", address = "Salt Lake City, Utah", annote = "pde" } @Book{marsden:hba76, author = "J. E. Marsden and M. F. McCracken", title = "the {H}opf {B}ifurcation and its {A}pplications", publisher = "Springer Verlag", year = "1976", annote = "BIF", } @Book{martin:mte81, author = "N. Martin and J. W. England", title = "Mathematical {T}heory of {E}ntropy", publisher = "Addison-Wesley", year = "1981", series = "Encyclopedia of Mathematics and Its Applications", volume = "12", } @Book{mawhin:tdm77, author = "J. Mawhin", title = "Topological Degree Methods in Nonlinear Boundary Value problems", publisher = "AMS", year = "1977", volume = "40", series = "CBMS Lecture Notes", address = "Providence", annote = "degree", } @Book{munkres:tfc75, author = "J. R. Munkres", title = "Topology: {A} First Course", publisher = "Prentice-Hall", year = "1975", address = "Englewood Cliffs, New Jersey", annote = "Top", } @Book{murray:mb89, author = "J. D. Murray", title = "Mathematical Biology", publisher = "Springer-Verlag", year = "1989", volume = "19", series = "Biomathematics", address = "New York", annote = "BIO", } % % book-n % @Book{nirenberg:tnf74, author = "L. Nirenberg", title = "Topics in {N}onlinear {F}unctional {A}nalysis", publisher = "Courant Institute Lecture Notes", year = "1974", annote = "BIF", } % % book-o % @Book{olver:alg86, author = "P. Olver", title = "Applications of {L}ie {G}roups to {D}ifferential {E}quations", publisher = "Springer-Verlag", year = "1986", address = "New York", annote = "Lie Groups, DE", } @Book{ortega:ipv88, author = "J.M. Ortega", title = "Introduction to {P}arallel and {V}ector {S}olution of {L}inear {S}ystems", publisher = "Plenum Press", year = "1988", address = "New York", annote = "numerical" } % % book-p % @Book{parlett:sep80, author = "B. N. Parlett", title = "The {S}ymmetric {E}igenvalue {P}roblem", publisher = "Prentice Hall", year = "1980", address = "Englewood Cliffs, NJ", annote = "eigenvalues" } @Book{pimbley:ebn69, author = "G. H. Pimbley", title = "Eigenfunction {B}ranches of {N}onlinear {O}perators and {T}heir {B}ifurcation", publisher = "Springer Verlag", year = "1969", volume = "104", series = "Lecture Notes in Math", annote = "BIF", } @Book{poincare:mnm92, author = "H. Poincar\'e", title = "Les m\'ethodes nouvelles de la m\'ecanique celeste", publisher = "Gauthier-Villars", year = "1892", volume = "1-3", } @Book{preston:imi83, author = "C. Preston", title = "Iterates of {M}aps on an {I}nterval", publisher = "Springer-Verlag", year = "1983", series = "Lecture Notes in Mathematics", volume = "999", } % % book-r % @Book{rabinowitz:apt77, author = "P. H. Rabinowitz", title = "Applications of {B}ifurcation {T}heory", publisher = "Academic Press", year = "1977", annote = "BIF", } @Book{roseau:vms84, author = "M. Roseau", title = "Vibrations in Mechanical Systems", publisher = "Springer", year = "1984", address = "Berlin", } % % book-s % @Book{sattinger:tsb73, author = "D. H. Sattinger", title = "Topics in stability and bifurcation theory", publisher = "Springer Verlag", year = "1973", volume = "309", series = "Lecture Notes in Math.", annote = "bifurcation", } @Book{sattinger:gtm79, author = "D. H. Sattinger", title = "Group {T}heoretic {M}ethods in {B}ifurcation {T}heory", publisher = "Springer Verlag", year = "1979", volume = "762", series = "Lecture Notes in Math.", annote = "BIF", } @Book{schechter:pfa71, author = "M. Schechter", title = "Principles of Functional Analysis", publisher = "Academic Press", year = "1971", address = "New York", } @Book{schwartz:nfa69, author = "J. T. Schwartz", title = "Nonlinear {F}unctional {A}nalysis", publisher = "Gordon and Breach", year = "1969", address = "New York", annote = "BIF", } @Book{smoller:swr82, author = "J. Smoller", title = "Shock {W}aves and {R}eaction-{D}iffusion {E}quations", publisher = "Springer Verlag", year = "1982", address = "Berlin", annote = "BIF", } @Book{sparrow:leb82, author = "C. Sparrow", title = "The Lorenz Equations: Bifurcation, Chaos and Strange Attractors", publisher = "SPR", year = "1982", volume = "41", series = "Appl. Math. Sci.", annote = "bifurcation, strange attractors", } @Book{sperb:mpa81, author = "R. Sperb", title = "Maximum {P}rinciples and {T}heir {A}pplications", publisher = "Springer Verlag", year = "1981", volume = "157", series = "Math. in Sci. and Eng.", address = "New York", annote = "PDE", } % % book-t % @Book{taylor:ifa67, author = "A. Taylor", title = "Introduction to {F}unctional {A}nalyis", publisher = "Wiley", year = "1967", address = "New York", } @Book{temam:idd88, author = "R. Temam", title = "Infinite-{D}imensional {D}ynamical {S}ystems in {M}echanics and {P}hysics", publisher = "Springer-Verlag", year = "1988", volume = "68", series = "Appl. Math. Sci.", address = "New York", annote = "PDE", } @Book{timoshenko:hsm83, author = "S. Timoshenko", title = "History of the {S}trength of {M}aterials", publisher = "Dover", year = "1983", address = "New York", } % % book-v % @Book{vanderbauwhede:lbs82, author = "A. Vanderbauwhede", title = "Local {B}ifurcation and {S}ymmetry", publisher = "Pitman", year = "1982", address = "London", series = "Research Notes in Math.", annote = "BIF", } % % book-w % @Book{wiggins:gbc88, author = "S. Wiggins", title = "Global {B}ifurcations and {C}haos", publisher = "Springer-Verlag", year = "1988", volume = "73", series = "Applied Mathematical Sciences", address = "New York", annote = "Bif", } @Book{whyburn:at42, author = "G. Whyburn", title = "Analytic {T}opolgy", publisher = "AMS", year = "1942", OPTaddress = "Providence", } % % book-x % % % book-y % @Book{yosida:fa80, author = "K. Yosida", title = "Functional {A}nalysis", publisher = "Springer-Verlag", year = "1980", address = "Berlin", annote = "Functional Analysis", } % % book-z % @Book{zeidler:nfa84I, author = "E. Zeidler", title = "Nonlinear {F}unctional {A}nalysis", publisher = "Springer Verlag", year = "1984", volume = "I", address = "New York", annote = "BIF", } @Book{zeidler:nfa88IIa, author = "E. Zeidler", title = "Nonlinear {F}unctional {A}nalysis", publisher = "Springer Verlag", year = "1988", volume = "IIa", address = "New York", annote = "BIF", } @Book{zeidler:nfa88IIb, author = "E. Zeidler", title = "Nonlinear {F}unctional {A}nalysis", publisher = "Springer Verlag", year = "1988", volume = "IIb", address = "New York", annote = "BIF", } @Book{zeidler:nfa89III, author = "E. Zeidler", title = "Nonlinear {F}unctional {A}nalysis", publisher = "Springer Verlag", year = "1989", volume = "III", address = "New York", annote = "BIF", } @Book{zeidler:nfa89IV, author = "E. Zeidler", title = "Nonlinear {F}unctional {A}nalysis", publisher = "Springer Verlag", year = "1989", volume = "IV and V", address = "New York", annote = "BIF", } %%% %%% inproceedings %%% @InProceedings{allgower:bac84, author = "E. L. Allgower", title = "Bifurcations arising in the calculation of critical points via homotopy methods", booktitle = "Numerical Methods for Bifurcation Problems, INSM 70", year = "1984", editor = "T. K\@upper and H. D. Mittelmann and H. Weber", publisher = "Birkh\@auser Verlag", annote = "bifurcations, homotopy", } @InProceedings{amann:pss78, author = "H. Amann", title = "Periodic solutions of semilinear parabolic equations", booktitle = "Nonlinear Analysis", year = "1978", editor = "L.Cesari, R. Kannan, H. Weinberger", pages = "", publisher = "Academic Press", address = "New York", } @InProceedings{aronson:rfp88, author = "D. G. Aronson", title = "Regularity of Flows in Porus Media: {A} Survey", booktitle = "Nonlinear Diffusion Equations and Their Equilibrium States I", year = "1988", editor = "W. M. Ni and L. A. Peletier and J. Serrin", pages = "35--49", publisher = "Springer-Verlag", address = "New York", } @InProceedings{beyn:dbp80, author = "W.-J. Beyn", title = "On discretization of bifurcation problems", booktitle = "Bifurcation Problems and Their Numerical Treatment", year = "1980", editor = "H. D. Mittelmann and H. Weber", publisher = "Birkh\@{a}user Verlag", note = "ISNM 54", annote = "bifurcation", } @InProceedings{beyn:des84, author = "W.-J. Beyn", title = "Defining equations for singular solutions and numerical applications", booktitle = "Numerical Methods for Bifurcation Problems", year = "1984", editor = "T. K\@upper and H. D. Mittelmann and H. Weber", publisher = "Birkh\@auser Verlag", note = "INSM 70", annote = "bifurcation", } @InProceedings{brezis:nee87, author = "H. Brezis", title = "Nonlinear elliptic equations involving the critical {S}obolev exponent - survey and perspectives", booktitle = "Directions in partial differential equations", year = "1987", editor = "M. Crandall and P. Rabinowitz and R. Turner", pages = "17--36", publisher = "Academic Press", address = "Boston", annote = "PDE" } @InProceedings{busse:stp81, author = "F. H. Busse", title = "Symmetry and transitions in patterns of cellular convection", booktitle = "Symmetries and Broken Symmetries", year = "1981", editor = "N. Boccara", address = "Idset-Paris", annote = "bifurcation analysis, two dimensional pattern", } @InCollection{cullum:ppc86, author = "J. Cullum and R. Willoughby", title = "A practical procedure for computing eigenvalues of large sparse nonsymmetric matrices", booktitle = "Large-Scale Eigenvalue Problems", publisher = "North Holland", year = "1986", editor = "J. Cullum and R. Willoughby", pages = "193-240", address = "Amsterdam", annote = "eigenvalues" } @InProceedings{doedel:cbb80, author = "E. J. Doedel and G. W. Reddien", title = "Computation of bifurcation branches using projection methods", booktitle = "Proc. 1980 U. S. Army Numerical Analysis and Computers Conference", year = "1980", pages = "223--231", organization = "ARO Report", annote = "bifurcation, numerical analysis", } @InProceedings{doedel:aut81, author = "E. J. Doedel", title = "{AUTO}: {A} program for the automatic bifurcation and analysis of autonomous systems", booktitle = "Proc. 10th Manitoba Conf. Num. Anal. and Comp.", year = "1981", pages = "265--284", annote = "bifurcation", } @InProceedings{doedel:nmh84, author = "E. J. Doedel and A. D. Jepson and H. B. Keller", title = "Numerical methods for {H}opf bifurcation and continuation of periodic solution paths", booktitle = "Computing Methods in Applied Sciences and Engineering VI", year = "1984", editor = "R. Glowinski and J. L. Lions", pages = "127--136", publisher = "North Holland Press", address = "Amsterdam", annote = "Hopf bifurcation, numerical analysis", } @InProceedings{keller:nsb77, author = "H. B. Keller", title = "Numerical solution of bifurcation and nonlinear eigenvalue problems", booktitle = "Applications of Bifurcation Theory", year = "1977", editor = "P. H. Rabinowitz", pages = "359--384", publisher = "Academic Press", annote = "bifurcation, numerical analysis", } @InProceedings{mawhin:qbs87, author = "J. Mawhin", title = "Qualitative behavior of the solutions of periodic first order scalar differential equations with strictly convex coercive nonlinearity", booktitle = "Dynamics of Infinite Dimensional Systems", year = "1987", editor = "Silhow and J. Hale", pages = "151-159", publisher = "Springer Verlag", address = "Berlin", annote = "DE" } @InProceedings{mittelmann:nmb80, author = "H. D. Mittelmann and H. Weber", title = "Numerical methods for bifurcation problems - {A} survey and classification", booktitle = "Bifurcation Problems and Their Numerical Solution", year = "1980", pages = "1--45", publisher = "Birkh\@{a}user Verlag", note = "ISNM 54", annote = "bifurcation, numerical analysis", } @InProceedings{rheinboldt:nap86, author = "W. C. Rheinboldt", title = "Numerical analysis of parametrized nonlinear equations", booktitle = "University of Arkansas Lecture Notes in the Mathematical Sciences", year = "1986", publisher = "Wiley-Interscience", annote = "numerical analysis, bifurcation", } @InProceedings{seydel:cas84, author = "R. Seydel", title = "A continuation algorithm with step control", booktitle = "Proc. Conf. on Numerical methods for bifurcation problems, Dortmund 1983", year = "1984", publisher = "Birkh\@{a}user Verlag", annote = "bifurcation, numerical analysis", } @InProceedings{weber:smb80, author = "H. Weber", title = "Shooting methods for bifurcation problems in ordinary differential equations", booktitle = "Bifurcation Problems and Their Numerical Solution", year = "1980", editor = "H. D. Mittelmann and H. Weber", pages = "185--210", publisher = "Birkh\@{a}user Verlag", note = "ISNM 54", annote = "bifurcation, numerical analysis", } %%% %%% articles %%% % % article-a % @Article{adler:te65, author = "R. L. Adler and A. G. Konheim and M. H. McAndrew", title = "Topological Entropy", journal = "Trans. Amer. Math. Soc.", year = "1965", volume = "114", month = feb, pages = "309--319", } @Article{alexandrov:uts56, author = "A. D. Alexandrov", title = "Uniqueness theorems for surfaces in the large {I}", journal = "Vestnik Leningrad Univ. Math. (Amer. Math. Soc. Translations)", year = "1956 (1962)", volume = "11 (21)", number = "19", pages = "5--17(341--354)", annote = "MC", } @Article{allgower:scm80, author = "E. Allgower and K. Georg", title = "Simplicial and continuation methods for approximating fixed points and solutions to systems of equations", journal = Srev, year = "1980", volume = "22", pages = "28--85", annote = "simplicial", } @Article{altman:fpt55, author = "M. Altman", title = "A fixed point theorem for completely continuous operators in {Banach} spaces", journal = "Bull. Acad. Polon. Sci. cl. III", year = "1955", volume = "3", number = "3", pages = "409--413", } @TechReport{amann:lsf74, author = "H. Amann", title = "Lectures on Some Fixed Point Theorems, Monografias de Matematica", institution = "IMPA", year = "1974", address = "Rio de Janeiro", } @Article{amann:fpe76, author = "H. Amann", title = "Fixed point equations and nonlinear eigenvalue problems in ordered {B}anach spaces", journal = Srev, year = "1976", volume = "18", pages = "620--709", annote = "BIF", } @Article{amann:smi76, author = "H. Amann", title = "Supersolutions, Monotone Iterations, and Stability", journal = "J. Diff. Eq.", year = "1976", volume = "21", pages = "363--377", annote = "PDE", } @Article{amann:utd73, author = "H. Amann and S. Weiss", title = "On the uniqueness of the topological degree", journal = "Math. Z.", year = "1973", volume = "130", pages = "39--54", annote = "Degree", } @Article{aronson:bic82, author = "D. G. Aronson and M. A. Chory and G. R. Hall and R. P. McGehee", title = "Bifurcations from an invariant circle for two-parameter families of maps of the plane: {A} computer-assisted study", journal = CMP, volume = "83", pages = "303--354", year = "1982", annote = "maps", } @Article{arnold:sdm61, author = "V. I. Arnold", title = "Small denominators {I}, {M}appings of the circumference onto itself", journal = "AMS Transl. Ser. 2", year = "1961", volume = "46", pages = "213--284", annote = "1D maps", } @Article{auchmuty:ban75, author = "J. F. G. Auchmuty and G. Nicolis", title = "Bifurcation analysis of nonlinear reaction-diffusion equations. - {I}. {E}volution equations and the steady state solutions", journal = "Bull. Math. Biol.", year = "1975", volume = "37", pages = "323--365", annote = "bifurcation analysis", } @Article{auchmuty:bar76, author = "J. F. G. Auchmuty and G. Nicolis", title = "Bifurcation analysis of reaction diffusion equations. - {III}. {C}hemical oscillations", journal = "Bull. Math. Biol.", year = "1976", volume = "38", pages = "325--350", annote = "bifurcation analysis", } % % article-b % @Article{bahri:een85, author = "A. Bahri and J. M. Coron", title = "Sur une \'{e}quation elliptique nonlin\'{e}aire avec l'exposant critique de {S}obolev", journal = "C. R. Acad. Sci. Paris", year = "1985", volume = "301", pages = "345--348", annote = "critical exponent", } @Article{bauer:abh77, author = "L. Bauer and H. B. Keller and E. L. Reiss", title = "Axisymmetric buckling of hollow spheres and hemispheres", journal = "Comm. Pure Appl. Math.", year = "1977", volume = "23", pages = "529--668", annote = "bifurcation", } @Article{bear:shb86, author = "S. Bear and T. Erneux", title = "Singular {H}opf bifurcation to relaxation oscillations", journal = SJAM, year = "1986", volume = "46", number = "5", pages = "721--739", annote = "Hopf bifurcation, relaxation oscillations", } @Article{bellout:sss90, author = "H. Bellout", title = "On some singular solutions of the equation {$\Delta u = -\lambda e^u$}", journal = "Comm. in PDE", year = "1990", volume = "15", number = "4", pages = "525--539", annote = "PDE", } @Article{benjamin:utc71, author = "T. Benjamin", title = "A unified theory of conjugate flows", journal = "Phil. Trans. Roy. Soc", year = "1971", volume = "269", number = "269", pages = "587--643", } @Article{boa:mss75, author = "J. A. Boa", title = "Multiple steady states in a model biochemical reaction", journal = "Stud. Appl. Maths.", year = "1975", volume = "54", pages = "9--15", annote = "bifurcation analysis", } @Article{boa:bld76, author = "J. A. Boa and D. S. Cohen", title = "Bifurcation of localised disturbances in a model biochemical reaction", journal = SJAM, year = "1976", volume = "30", pages = "123--135", annote = "bifurcation analysis", } @Article{bohme:lvn70, author = "R. B{\"o}hme", title = "Die {L}{\"o}sungen der {V}erzweigungsgleichungen f{\"u}r nichtlineare {E}igenwertprobleme", journal = "Math. Z.", year = "1970", volume = "127", pages = "105--126", annote = "PDE", } @Article{bona:fpt72, author = "J. Bona", title = "Fixed point theorems for Frechet spaces", journal = "Springer Lecture Notes in Math", year = "1972", volume = "280", number = "280", pages = "219--222", } @Article{bowen:ege71, author = "R. Bowen", title = "Entropy for Group Endomorphisms and Homogeneous Spaces", journal = "Trans.\ Amer.\ Math.\ Soc.", year = "1971", volume = "153", month = jan, pages = "401--414", } @Article{bowen:ten73, author = "R. Bowen", title = "Topological Entropy for Noncompact Sets", journal = "Trans.\ Amer.\ Math.\ Soc.", year = "1973", volume = "184", month = oct, pages = "125--136", } @Article{bratu:ein14, author = "G. Bratu", title = "Sur les equations integrales non lineares", journal = "Bull. Soc. Math. de France", year = "1914", volume = "42", pages = "113--142", annote = "Gelfand or Bratu problem", } @Article{brezis:ueb91, author = "H. Brezis and F. Merle", title = "Uniform estimates and blow-up behavior for solutions of {$-\Delta u = V(x)e^u$} in two dimensions", journal = "Comm. in PDE", year = "1991", volume = "16", number = "8 \&9", pages = "1223--1253", annote = "PDE", } @Article{brezis:psn83, author = "H. Brezis and L. Nirenberg", title = "Positive solutions of nonlinear elliptic equations involving critical {S}obolev exponents", journal = "Comm. Pure. Appl. Math.", year = "1983", volume = "41", pages = "437--477", annote = "PDE", } @TechReport{brown:hkm87, author = "P. Brown and Y. Saad", title = "Hybrid {K}rylov methods for nonlinear systems of equations", institution = "LLNL", year = "1987", number = "ucrl-97645", month = nov, annote = "conjugate gradient", } @Article{budd:see87, author = "C. Budd and J. Norbury", title = "Semilinear elliptic equations and supercritical growth", journal = "J. Diff. Eq.", year = "1987", volume = "68", pages = "169--197", annote = "PDE", } @Article{busse:sfa67, author = "F. H. Busse", title = "The stability of finite amplitude cellular convection and its relation to an extremum principle", journal = "J. Fluid Mech.", year = "1967", volume = "30", pages = "625--649", annote = "bifurcation analysis, two dimensional pattern", } @Article{busse:pcs75, author = "F. H. Busse", title = "Patterns of convection in spherical shells", journal = "J. Fluid Mech.", year = "1975", volume = "72", pages = "67--85", annote = "bifurcation analysis, two dimensional pattern", } % % article-c % @Article{caffarelli:asl89, author = "L. Caffarelli and B. Gidas and J. Spruck", title = "Asymptotic symmetry and local behavior of semilinear elliptic equations with critical Sobolev growth", journal = "Comm. Pure Appl. Math.", year = "1989", volume = "42", pages = "271--297", annote = "PDE", } @Article{chaundy:csd36, author = "T. W. Chaundy and E. Phillips", title = "The convergence of sequences defined by quadratic recurrence-formulae", journal = "Quart. J. Math.", year = "1936", pages = "74--80", annote = "1D maps", } @Article{cosner:gls88, author = "C. Cosner and K. Schmitt", title = "On the geometry of level sets of positive solutions of semilinear elliptic equations", journal = "Rocky Mountain J. of Math.", year = "1988", volume = "18", number = "2", pages = "277--286", annote = "PDE", } @Article{crandall:bse71, author = "M. G. Crandall and P. H. Rabinowitz", title = "Bifurcation from simple eigenvalues", journal = "J. Func. Anal.", year = "1971", volume = "8", pages = "231--340", annote = "bifurcation", } @Article{crandall:cvm75, author = "M. G. Crandall and P. H. Rabinowitz", title = "Some continuation and variation methods for positive solutions of nonlinear elliptic eigenvalue problems", journal = "Arch. Rat. Mech. Anal.", year = "1975", volume = "58", number = "3", pages = "208--218", annote = "bifurcation", } @Article{crandall:hbt76, author = "M. G. Crandall and P. H. Rabinowitz", title = "The {H}opf bifurcation theorem", journal = "Arch. Rat. Mech. Anal.", year = "1976", annote = "Hopf bifurcation", } @InProceedings{cronin:fpt64, author = "J. Cronin", title = "Fixed Points and Topological Degree in Nonlinear Analysis", booktitle = "Math. Surveys No. 11", year = "1964", organization = "Amer. Math. Soc.", address = "Providence", } @Article{cullum:gnl89, author = "J. Cullum and W. Kerner and R. Willoughby", title = "A generalized nonsymmetric {L}anczos procedure", journal = "Computer Physics Comm.", year = "1989", volume = "53", pages = "19-48", annote = "eigenvalues" } % % article-d % @Article{dancer:pss87, author = "N. Dancer and K. Schmitt", title = "On positive solutions of semilinear elliptic equations", journal = "PAMS", year = "1987", volume = "101", pages = "445--452", annote = "PDE", } @Article{defigueiredo:aee82, author = "D. G. de Figueiredo and P. L. Lions and R. D. Nussbaum", title = "A priori estimates and existence of positive solutions of semilinear elliptic equations", journal = "J. Math. pures et appl.", year = "1982", volume = "61", pages = "41--63", annote = "PDE", } @Article{dellwo:bi82, author = "D. Dellwo and H. B. Keller and B. J. Matkowsky and E. L. Reiss", title = "On the birth of isolas", journal = SJAM, year = "1982", volume = "42", number = "5", pages = "956--963", annote = "isolas, bifurcation", } @Article{dickey:bpn76, author = "R. W. Dickey", title = "Bifurcation {P}roblems in {N}onlinear {E}lasticity", journal = "Pitman Research Notes in Math.", year = "1976", address = "London", annote = "BIF", } @Article{doedel:ntb82, author = "E. J. Doedel and P. C. Leung", title = "Numerical techniques for bifurcation problems in delay equations", journal = "Cong. Num.", year = "1982", volume = "34", pages = "225--237", note = "Proc. 11th Manitoba Conf. on Num. Math. and Comp., Univ. of Manitoba, Winnipeg, Canada", annote = "bifurcation, numerical analysis", } @Article{doedel:ncp83, author = "E. J. Doedel and R. F. Heinemann", title = "Numerical computation of periodic solution branches and oscillatory dynamics of the stirred tank reactor with ${A} \rightarrow {B} \rightarrow {C}$ reactions", journal = "Chem. Eng. Sci.", year = "1983", volume = "38", number = "9", pages = "1493--1499", annote = "Numerical bifurcation", } @TechReport{doedel:aut86, author = "E. J. Doedel and J. P. Kernevez", title = "{AUTO}: Software for continuation and bifurcation problems in ordinary differential equations with applications", institution = "Caltech", year = "1986", type = "Applied Math", annote = "auto" } @Article{doedel:bvh87, author = "E. J. Doedel and J. F. Magnan and E. L. Reiss", title = "Bending of vertical {H}opf bifurcation branches in rotating thermal convection with an imperfection", journal = "Phys. Rev. A.", year = "1987", note = "in press", annote = "Hopf bifurcation", } @Article{doedel:nac91, author = "E. J. Doedel and H. Keller and J. P. Kernevez", title = "Numerical analysis and control of bifurcation problems {I}, bifurcation in finite dimensions ", journal = "International journal of bifurcation and chaos", year = "1991", volume = "1", number = "3", pages = "493-520", annote = "auto" } @Article{dugundji:ett51, author = "J. Dugundji", title = "An extension of {Tietze's Theorem}", journal = "Pac. J. Math", year = "1951", volume = "1", pages = "353--367", annote = "Topology", } % % article-e % @Article{erneux:bdm79, author = "T. Erneux and M. Herchkowitz-Kaufman", title = "The bifurcation diagram of a model chemical reaction. {II}. 2-dimensional time periodic patterns", journal = "Bull. Math. Biol.", year = "1979", volume = "41", pages = "767--790", annote = "bifurcation analysis, two dimensional pattern", } % % article-f % @TechReport{fournier:sfp76, author = "F. Fournier and H. O. Peitgen", title = "On some fixed point principles for cones in linear spaces", institution = "Universit{\"{a}}t", year = "1976", number = "86", } @TechReport{freund:qmr90, author = "R. W. Freund and N. M. Nachtigal", title = "QMR: a Quasi-Minimal Residual Method for Non-Hermitian Linear System", institution = "NASA Ames Research Center", year = "December 1990", number = "90.15", } @TechReport{freund:ila91, author = "R. W. Freund and Martin H. Gutknecht and N. M. Nachtigal", title = "An Implementation of the Look-Ahead Lanczos Algorithm for Non-Hermitian Matrices", institution = "NASA Ames Research Center", year = "April 1991", number = "91.09", annote = "QMR" } % % article-g % @Article{garaizar:epr87, author = "X. Garaizar", title = "Existence of positive radial solutions for semilinear elliptic equations in the annulus", journal = "J. Diff. Eq.", year = "1987", volume = "70", pages = "69--92", annote = "PDE", } @Article{gelfand:spt63, author = "I. M. Gelfand", title = "Some problems in the theory of quasilinear equations", journal = "Amer. Math. Soc. Transl.", year = "1963", volume = "29", pages = "295--381", annote = "gelfand problem", } @Article{gidas:srp79, author = "B. Gidas and W. Ni and L. Nirenberg", title = "Symmetry and related properties via the maximum principle", journal = "Comm. Math. Phys.", year = "1979", volume = "68", pages = "209--243", annote = "Symmetry, PDE", } @Article{gidas:abp81, author = "B. Gidas and J. Spruck", title = "A priori bounds for positive solutions of nonlinear elliptic equations", journal = "Comm. in PDE", year = "1981", volume = "6", number = "8", pages = "883--901", annote = "PDE", } @Article{glowinski:ccg85, author = "R. Glowinski and H. B. Keller and L. Reinhart", title = "Continuation-conjugate gradient methods for the least square solution of nonlinear boundary value problems", journal = SJSS, year = "1985", volume = "6", number = "4", pages = "793--832", month = oct, annote = "conjugate gradient", } @Article{golubitsky:cud81, author = "M. Golubitsky and W. F. Langford", title = "Classification and unfoldings of degenerate {H}opf bifurcations", journal = JDE, year = "1981", volume = "41", number = "3", pages = "375--415", annote = "Hopf bifurcations", } @Article{gossez:pss91, author = "J. P. Gossez and P. P. Omari", title = "Periodic solutions of a second order ordinary differential equation: a necessary and sufficient condition for nonresonance", journal = JDE, year = "1991", volume = "94", OPTnumber = "", pages = "67--82", OPTmonth = "", OPTnote = "", OPTkeyword = "", OPTannote = "" } @Article{griewank:chp83, author = "A. Griewank and G. W. Reddien", title = "The calculation of {H}opf points by a direct method", journal = "IMA J. Numer. Anal.", year = "1983", volume = "3", pages = "295--303", annote = "Hopf bifurcation, numerical analysis", } @Article{guckenheimer:sdi79, author = "J. Guckenheimer", title = "Sensitive Dependence to Initial Conditions for One Dimensional Maps", journal = "Commun. Math. Phys.", year = "1979", volume = "70", pages = "133--160", } @Article{gustafson:nsb72, author = "G. B. Gustafson and K. Schmitt", title = "Nonzero solutions of boundary value problems for second order ordinary and delaying differential equations", journal = j-JDE, year = "1972", volume = "12", number = "12", pages = "125--147", } @Article{glendinning:lgb84, author = "P. Glendinning and C. Sparrow", title = "Local and global behavior near homoclinic orbits", journal = "Jour. Stat. Phys.", volume = "35", pages = "645--696", year = "1984", annote = "global bifurcation", } % % article-h % @Article{hale:cdp74, author = "J. Hale and J. Mawhin", title = "Coincidence and degree and periodic solution- of neutral equations", journal = j-JDE, year = "1974", volume = "15", number = "15", pages = "295--307", } @Article{heinemann:mso81, author = "R. F. Heinemann and A. B. Poore", title = "Multiplicity, stability, and oscillatory dynamics of the tubular reactor", journal = "Chem. Eng. Sci.", year = "1981", volume = "36", pages = "1411", annote = "bifurcation, nonlinear oscillations", } @Article{heinz:eat59, author = "E. Heinz", title = "An elementary analytic theory of the degree of mapping in n-dimensional Euclidean space", journal = "J. Math. Mech.", year = "1959", volume = "8", pages = "231--247", annote = "degree", } @Article{heinz:ebs92, author = "H. P. Heinz and T {K\"{u}}pper and C. A. Stuart", title = "Existence and bifurcation of solutions for nonlinear perturbations of the periodic {S}chr{\"{o}}dinger equation", journal = "JDE", year = "1992", volume = "100", pages = "341--354", annote = "schrodinger" } @Article{hess:mps81, author = "P. Hess", title = "On multiple positive solutions of nonlinear eigenvalue problems", journal = "Comm. PDE", year = "1981", volume = "6", pages = "951--961", annote = "PDE", } @Article{hiernaux:cpc79, author = "J. Hiernaux and T. Erneux", title = "Chemical patterns in circular morphogenetic fields", journal = "Bull. Math. Biol.", year = "1979", volume = "41", pages = "461--468", annote = "bifurcation analysis, two dimensional pattern", } @Article{hlavavcek:msa72, author = "V. Hlavavcek and M. Kubicek and K. Visnak", title = "Multiplicity and stability analysis of a continuous stirred tank reactor with exothermic consecutive reactions ${A} \rightarrow {B} \rightarrow {C}$", journal = "Chem. Eng. Sci.", year = "1972", volume = "27", pages = "719--742", annote = "bifurcation, nonlinear oscillations", } @Article{holmes:bdf78, author = "P. Holmes and J. Marsden", title = "Bifurcation to divergence and flutter in flow-induced oscillations: {A}n infinite dimensional analysis", journal = "Automatica", year = "1978", volume = "14", pages = "367--384", annote = "bifurcation", } @Article{holodniok:dac84, author = "M. Holodniok and M. Kubicek", title = "{DERPER} - {A}n algorithm for the continuation of periodic solutions in ordinary differential equations", journal = "J. Comp. Phys.", year = "1984", volume = "55", number = "2", pages = "254--267", annote = "bifurcation, numerical analysis", } @Article{hopf:ael42, author = "E. Hopf", title = "{A}bzweigung einerperiodischen {L}{\"o}sung von einer station{\"a}ren {L}{\"o}sung eines {D}ifferentialsystems", journal = "Ber. Math. Phys.", year = "1942", volume = "94", pages = "1--22", } % % article-i % % % article-j % @Article{jepson:fst85, author = "A. Jepson and A. Spence", title = "Folds in solutions of two parameter systems and their calculation: {P}art {I}", journal = "SIAM J. Numer. Anal.", year = "1985", volume = "22", number = "2", pages = "347--368", annote = "bifurcation, numerical analysis", } @Article{joseph:qdp73, author = "D. D. Joseph and T. S. Lundgren", title = "Quasilinear {D}irichlet problems driven by positive sources", journal = "Arch. Rat. Mech. Appl.", year = "1973", volume = "49", pages = "241--269", annote = "PDE", } @Article{joseph:ndi70, author = "D. D. Joseph and E. M. Sparrow", title = "Nonlinear diffusion induced by nonlinear sources", journal = "Quart. Appl. Math.", year = "1970", volume = "28", pages = "327--342", annote = "nonlinear heat flow", } % % article-k % @Article{kazdan:cfc74, author = "J. L. Kazdan and F. W. Warner", title = "Curvature functions for compact 2-manifolds", journal = "Ann. of Math.", year = "1974", volume = "99", pages = "14--47", annote = "Riemannian Geometry", } @Article{keller:ipm72, author = "H. B. Keller and W. F. Langford", title = "Iterations, perturbations and multiplicities for nonlinear bifurcation problems", journal = "Arch. Rat. Mech. Anal.", year = "1972", volume = "48", pages = "83--108", annote = "bifurcation", } @Article{kevrekidis:nci85, author = "I. G. Kevrekidis and R. Aris and L. D. Schmidt and S. Pelikan", title = "Numerical computation of invariant circles of maps", journal = "Physica", year = "1985", volume = "16D", pages = "243--251", annote = "maps, discrete dynamical systems", } @Article{krein:lol62, author = "M. Krein and M. Rutman", title = "Linear operators leaving invariant a cone in a Banach space", journal = "AMS Transl.", year = "1962", volume = "10", pages = "199--325", annote = "Functional", } @Article{korevaar:csc87, author = "N. J. Korevaar and J. L. Lewis", title = "Convex solutions of certain elliptic equations have constant rank hessians", journal = "Arch. Rat. Mech. and Anal.", year = "1987", volume = "97", number = "1", pages = "19--32", annote = "PDE", } @Article{korevaar:cls90, author = "N. J. Korevaar", title = "Convexity of level sets for solutions to elliptic ring problems", journal = "Comm. in PDE", year = "1990", volume = "15", number = "4", pages = "541--556", annote = "PDE", } @TechReport{kubicek:nth79, author = "M. Kubicek", title = "The numerical treatment of {H}opf bifurcation problems for {ODE}'s", institution = "where", year = "1979", type = "Technical Report", annote = "Hopf bifurcation, numerical analysis", } @Article{kubicek:ehb84, author = "M. Kubicek and M. Holodniok", title = "Evaluation of {H}opf bifurcation points in parabolic equations describing heat and mass transfer in chemical reactors", journal = "Chem. Eng. Sci.", year = "1984", volume = "39", number = "3", pages = "593--599", annote = "Hopf bifurcation, numerical analysis", } % % article-l % @Article{landesman:npl70, author = "E. Landesman and A. Lazer", title = "Nonlinear perturbations of linear elliptic boundary value problems", journal = "J. Math. Mech.", year = "1970", OPTvolume = "19", OPTpages = "609-623", OPTannote = "PDE", } @Article{langford:nsb77, author = "W. F. Langford", title = "Numerical solution of bifurcation problems for ordinary differential equations", journal = "Numerische Mathematik", year = "1977", volume = "28", pages = "171--190", annote = "bifurcation, numerical analysis", } @Article{langford:pss79, author = "W. F. Langford", title = "Periodic and steady state mode interactions lead to tori", journal = SJAM, year = "1979", volume = "34", number = "1", pages = "22--48", annote = "bifurcation", } @Article{langford:bps73, author = "O. Lanford", title = "Bifurcation of periodic solutions into invariant tori: the work of {R}uelle and {T}akens", journal = "Lect. Notes Math.", year = "1973", volume = "322", pages = "159", annote = "dynamical systems, maps, bifurcation", } @Article{lazer:bpf69, author = "A. Lazer and D. Leach", title = "Bounded perturbations of forced harmonic oscillations at resonance", journal = "Ann. Mat. Pura Appl.", year = "1969", volume = "72", pages = "49--68", annote = "perturbation", } @Article{leray:tef34, author = "J. Leray and J. Schauder", title = "Topologie et {\'e}quations fonctionelles", journal = "Ann. Sci. {\'E}cole Norm. Sup.", year = "1934", volume = "51", pages = "45--78", annote = "degree", } @TechReport{li:srn79, author = "T.-Y. Li and J. A. Yorke", title = "A simple reliable numerical algorithm for following homotopy paths", institution = "Univ. of Wisc.", year = "1979", type = "MRC Report 1984", annote = "bifurcation, numerical analysis", } @Article{lin:epr89, author = "S. S. Lin", title = "On the existence of positive radial solutions for nonlinear elliptic equations in annular domains", journal = "J. Diff. Eq.", year = "1989", volume = "81", pages = "221--233", annote = "PDE", } @Article{lin:prs90, author = "S. S. Lin", title = "Positive radial solutions and non-radial bifurcation for semilinear elliptic equations in annular domains", journal = "J. Diff. Eq.", year = "1990", volume = "86", pages = "367--391", annote = "BIF", } @Article{lin:emp91, author = "S. S. Lin and F. M. Pai", title = "Existence and multiplicity of positive radial solutions for semilinear elliptic equations in annular domains", journal = SJAM, year = "1991", volume = "22", number = "6", pages = "1500--1515", annote = "PDE", } @Article{lions:eps82, author = "P. L. Lions", title = "On the existence of positive solutions of semilinear elliptic equations", journal = Srev, year = "1982", volume = "24", number = "4", pages = "441-467", annote = "continua" } @Article{liouville:edp53, author = "J. Liouville", title = "Sur l'equation aux d\'{e}riv\'{e}es partielles {$\frac{\partial^2\ln\lambda}{\partial u\partial v}\pm 2\lambda a^2 =0$}", journal = "J. de Math", year = "1853", volume = "18", pages = "71--72", annote = "Gelfand Bratu", } @Article{lorenz:pdc64, author = "E. N. Lorenz", title = "The problem of deducing the climate from the governing equation", journal = "Tellus", year = "1964", volume = "16", pages = "1--11", annote = "1D maps", } % % article-m % @Article{maini:bsh91, author = "M. R. Myerscough, K. H. Winters P. K. Maini and J. D. Murray", title = "Bifurcating spatially heterogeneous solutions in a chemotaxis model for biological pattern generation", journal = "Bulletin of Mathematical Biology", year = "1991", volume = "53", pages = "701--719", annote = "Bio", } @Article{margolis:bpb80, author = "S. B. Margolis", title = "Bifurcation phenomena in burner-stabilized premixed flames", journal = "Comb. Sc. and Tech.", year = "1980", volume = "22", pages = "143--169", annote = "bifurcation, combustion", } @Article{markus:odl56, author = "L. Markus and R. Moore", title = "Oscillation and disconjugacy for linear differential equations with almost periodic coeficients", journal = "Acta Math.", year = "1956", volume = "96", pages = "99-123", annote = "DE" } @Article{matkowsky:snd70, author = "B. J. Matkowsky", title = "A simple non-linear dynamic stability problem", journal = "Bull. Amer. Math. Soc.", year = "1970", volume = "76", pages = "620--625", annote = "bifurcation analysis", } @Article{mawhin:etn72, author = "J. Mawhin", title = "Equivalence theorems for nonlinear opoerator equations and coincidence degree theory for some mappings in locally convex topological vector spaces", journal = j-JDE, year = "1972", volume = "1", number = "1", pages = "610--636", } @Article{mawhin:foo87, author = "J. Mawhin", title = "First order ordinary differential equations with several periodic solutions", journal = "J. Appl. Math.", year = "1987", volume = "38", pages = "257-265", annote = "DE" } @Article{mawhin:ltp88, author = "J. Mawhin and K. Schmitt", title = "Landesman-Lazer type problems at an eigenvalue of odd multiplicity", journal = "Results in Math.", year = "1988", volume = "14", pages = "138--146", annote = "Landesman-Lazer", } @Article{mawhin:nep90, author = "J. Mawhin and K. Schmitt", title = "Nonlinear eigenvalue problems with the parameter near resonance", journal = "Ann. Polon. Math.", year = "1990", volume = "51", pages = "241--248", annote = "de", } @Article{mawhin:rat77, author = "J. Mawhin and K. Schmitt", title = "Rothe and Altman type coincidence theorems and applications to differential equations", journal = j-NLA, year = "1977", volume = "1", number = "1", pages = "151--160", } @Article{meijerink:ism77, author = "J. Meijerink and H. A. van der Vorst", year = "1977", title = "An iterative solution method for linear systems of which the coefficient matrix is a symmetric {M}-matrix", journal = "Math. Comp.", volume = "31", pages = "148--162", } @Article{milnor:ca85, author = "J. Milnor", title = "On the Concept of Attractor", journal = "Comm. Math. Phys.", year = "1985", volume = "99", pages = "177--195", } @Article{milnor:cac85, author = "J. Milnor", title = "On the Concept of Attractor: Correction and Remarks", journal = "Commun. Math. Phys.", year = "1985", volume = "102", pages = "517--519", } @Article{misiurewicz:epm80, author = "M. Misiurewicz and W. Szlenk", title = "Entropy of Piecewise Monotone Mappings", journal = "Studia Math.", year = "1980", volume = "67", pages = "45--63", } @Article{murray:mmg88, author = "J. D. Murray and P. K. Maini and R. T. Tranquillo", title = "Mechanochemical models for generating biological pattern and form in development", journal = "Physics Reports", year = "1988", volume = "171", pages = "59--84", annote = "Bio", } @Article{murray:mmm83, author = "J. D. Murray and G. F. Oster and A. K. Harris", title = "A mechanichal model for mesenchymal morphogenesis", journal = "J. Math. Biology", year = "1983", volume = "17", pages = "125--129", annote = "Bio", } @Article{murray:nag86, author = "J. D. Murray and P. K. Maini", title = "A new approach to the generation of pattern and form in embriology", journal = "Sci. Prog.", year = "1986", volume = "70", pages = "539--553", annote = "Bio", } @Article{murray:ctm84, author = "J. D. Murray and G. F. Oster", title = "Cell traction models for generating pattern and form in morphogenesis", journal = "J. Math. Biol.", year = "1984", volume = "19", pages = "265--279", annote = "Bio", } @Article{murray:gbp84, author = "J. D. Murray and G. F. Oster", title = "Generation of biological pattern and form", journal = "{I}{M}{A} Journal of Mathematics Applied in Medicine and Biology", year = "1984", volume = "1", pages = "51--75", annote = "Bio", } % % article-n % @Article{nagumo:tdm51, author = "M. Nagumo", title = "A theory of degree of mapping based on infinitesimal analysis", journal = "Amer. J. Math.", year = "1951", volume = "73", pages = "485--496", annote = "degree", } @Article{ni:unp85, author = "W. M. Ni and R. Nussbaum", title = "Uniqueness and non-uniqueness for positive radial solutions of {$\Delta u+f(u,r)=0$}", journal = "J. Diff. Eq.", year = "1985", volume = "50", pages = "289--304", annote = "PDE", } % % article-o % @Article{opial:spp59, author = "Z. Opial", title = "Sur les solutions presque--p\'{e}riodiques des \'{e}quations diff\'{e}r\-entielles du premier et du second ordre", journal = "Ann. Polon. Math.", year = "1959", volume = "7", pages = "51-61", annote = "DE" } @Article{oster:mam83, author = "G. F. Oster and J. D. Murray and A. K. Harris", title = "Mechanical aspects of mesenchymal morphogenesis", journal = "J. Embryol. exp. Morph.", year = "1983", volume = "78", pages = "83--125", annote = "Bio", } @Article{oster:pfm89, author = "G. F. Oster and J. D. Murray", title = "Pattern formation models and developmental constraints", journal = "The Journal of Experimental Zoology", year = "1989", volume = "251", pages = "186--202", annote = "Bio", } @Article{ostrowski:crqi57, author = "A. M. Ostrowski", title = "On the convergence of the {R}ayleigh quotient iteration for the computation of the characteristic roots and vectors. {I}", journal = ARCH, year = "1957/58", volume = "1", pages = "233-241", annote = "RQI" } @Article{ostrowski:crqii58, author = "A. M. Ostrowski", title = "On the convergence of the {R}ayleigh quotient iteration for the computation of the characteristic roots and vectors. {II}", journal = ARCH, year = "1958/59", volume = "2", pages = "421-428", annote = "RQI" } @Article{ostrowski:crqiii59, author = "A. M. Ostrowski", title = "On the convergence of the {R}ayleigh quotient iteration for the computation of the characteristic roots and vectors. {III}", journal = ARCH, year = "1959", volume = "3", pages = "325-340", annote = "RQI" } @Article{ostrowski:crqiv59, author = "A. M. Ostrowski", title = "On the convergence of the {R}ayleigh quotient iteration for the computation of the characteristic roots and vectors. {IV}", journal = ARCH, year = "1959", volume = "3", pages = "341-347", annote = "RQI" } @Article{ostrowski:crqv59, author = "A. M. Ostrowski", title = "On the convergence of the {R}ayleigh quotient iteration for the computation of the characteristic roots and vectors. {V}", journal = ARCH, year = "1959", volume = "3", pages = "472-481", annote = "RQI" } @Article{ostrowski:crqvi60, author = "A. M. Ostrowski", title = "On the convergence of the {R}ayleigh quotient iteration for the computation of the characteristic roots and vectors. {VI}", journal = ARCH, year = "1959/60", volume = "4", pages = "153-165", annote = "RQI" } % % article-p % @Article{parlett:rqi74, author = "B. N. Parlett", title = "The {R}ayleigh quotient iteration and some generalizations for nonnormal matrices", journal = "Math. Comp.", year = "1974", volume = "28", pages = "679-693", annote = "eigenvalues" } @Article{payne:bsc81, author = "L. E. Payne", title = "Bounds for solutions of a class of quasilinear elliptic boundary value problems in terms of the torsion function", journal = "Proc. Roy. Soc. Edinburgh", year = "1981", volume = "88A", pages = "251--265", annote = "PDE", } @Article{peitgen:tpg82, author = "H. Peitgen", title = "Toplogische Perturbationen beim globalen numerischen Studium nichtlinearer Eigenwert und Verzweigungsprobleme", journal = "Jber. Deutsch. Math. Ver.", year = "1982", volume = "84", pages = "107--162", } @Article{peitgen:nep81, author = "H. Peitgen and D. Saupe and K. Schmitt", title = "Nonlinear eigenvalue problems versus their finite difference approximations: Numerically irrelevant solutions.", journal = "J. reine angew. Mathematik", year = "1981", volume = "322", pages = "74--117", annote = "numerical artifacts", } @Article{peitgen:pgt80, author = "H. Peitgen and K. Schmitt", title = "Perturbations globales topologiques des problemes nonlineaires de valeur propre", journal = "Comptes Rendues Acad. Sc. Paris", year = "1980", volume = "291", pages = "271--274", } @Article{peitgen:gtp83, author = "H. Peitgen and K. Schmitt", title = "Global topological perturbations of nonlinear eigenvalue problems", journal = "Math. Meth. Appl. Sci.", year = "1983", volume = "5", pages = "376--378", } @Article{peitgen:gae84, author = "H. Peitgen and K. Schmitt", title = "Global analysis of elliptic two parameter eigenvalue problems", journal = "TAMS", year = "1984", volume = "283", number = "57-95", } @Article{peletier:oe86, author = "L. A. Peletier and D. Terman and F. B. Weissler", title = "On the equation {$\Delta u + \frac{1}{2}x\cdot\nabla u + f(u) = 0$}", journal = "Arch. Rat. Mech. Anal.", year = "1986", volume = "94", number = "1", pages = "83--99", } @Article{poore:tah76, author = "A. B. Poore", title = "On the theory and application of the {H}opf-{F}riedrichs bifurcation theory", journal = "Arch. Rat. Mech. Anal.", year = "1976", volume = "60", pages = "371--393", annote = "Hopf bifurcation", } @Article{pohozaev:ee65, author = "S. I. Pohozaev", title = "Eigenfunctions of the equation {$\Delta u + \lambda f(u) = 0$}", journal = "Soviet Math. Dokl.", year = "1965", volume = "6", pages = "1408--1411", annote = "PDE", } @Article{pucci:gvi86, author = "P. Pucci and J. Serrin", title = "A general variational identity", journal = "Indiana Univ. Math. J.", year = "1986", volume = "35", number = "3", pages = "681--703", annote = "pohozaev", } % % article-q % % % article-r % @Article{rabinowitz:san73, author = "P. H. Rabinowitz", title = "Some aspects of nonlinear eigenvalue problems", journal = "Rocky Mountain J. Math.", year = "1973", volume = "3", pages = "161--202", annote = "BIF", } @Article{rellich:der40, author = "F. Rellich", title = "Darstellung der {E}igenwerte von {$\Delta u + \lambda u = 0$} durch ein {R}andintegral", journal = "Math Z.", year = "1940", volume = "46", pages = "635--636", annote = "rellich identity", } @Article{rheinboldt:nmc78, author = "W. C. Rheinboldt", title = "Numerical methods for a class of finite dimensional bifurcation problems", journal = "SIAM J. Numer. Anal.", year = "1978", volume = "15", pages = "1--11", annote = "bifurcation, numerical analysis", } @Article{rheinboldt:ccb82, author = "W. C. Rheinboldt", title = "Computation of critical boundaries on equilibrium manifolds", journal = "SIAM J. Numer. Anal.", year = "1982", volume = "19", number = "3", pages = "653--669", annote = "numerical analysis, bifurcation", } @Article{rothe:tto37, author = "E. Rothe", title = "Fur Theorie der topologischen Ordnung und der Vektorfelder in {Banach} {R\"{a}}umen", journal = "Compositio Math", year = "1937", volume = "5", number = "5", pages = "177--197", } @Article{ruelle:nt69, author = "D. Ruelle and F. Takens", title = "On the nature of turbulence", journal = "Comm. Math. Phys.", year = "1969", volume = "20", pages = "167", annote = "bifurcation,dynamical systems,turbulence", } % % article-s % @Article{saad:gmr86, author = "Y. Saad and M. H. Schultz", title = "{GMRES}: {A} generalized minimal residual algorithm for solving nonsymmetric linear systems", journal = SJSS, year = "1986", volume = "7", pages = "856--869", annote = "gmres", } @Article{schaaf:cns88, author = "R. Schaaf and K. Schmitt", title = "A class of nonlinear Sturm-Liouville problems with infinitely many solutions", journal = "TAMS", year = "1988", volume = "306", pages = "853--859", } @Article{schiaffino:psc84, author = "A. Schiaffino and K. Schmitt", title = "Periodic solutions of a class of nonlinear evolution equations", journal = "Ann. Mat. Pura Appl.", year = "1984", volume = "137", pages = "265--272", } @Article{schmitt:bvp78, author = "K. Schmitt", title = "Boundary value problems for quasilinear elliptic partial differential equations", journal = "Nonl. Anal.", year = "1978", volume = "2", pages = "263--309", } @Article{schmitt:bvp86, author = "K. Schmitt", title = "Boundary value problems with jumping nonlinearities", journal = "Rocky Mtn. J. Math.", year = "1986", volume = "16", pages = "481--496", } @Article{schmitt:aps92, author = "K. Schmitt and J. Ward", title = "Almost periodic solutions of nonlinear second order differential equations", journal = "Results in Math.", year = "1992", volume = "21", pages = "190-199", annote = "DE" } @Article{schmitt:aaa93, author = "K. Schmitt and J. Ward", title = "Attractors and almost periodic solutions of semilinear parabolic equations", journal = "to appear", year = "1993", annote = "PDE" } @Article{segel:qpm62, author = "L. A. Segel and J. T. Stuart", title = "On the question of the preferred mode in cellular thermal convection", journal = "J. Fluid Mech.", year = "1962", volume = "13", pages = "289--305", annote = "bifurcation analysis", } @Article{seydel:ncb79a, author = "R. Seydel", title = "Numerical computation of branch points in nonlinear equations", journal = "Numer. Math.", year = "1979", volume = "33", pages = "339--352", annote = "bifurcation, numerical analysis", } @Article{seydel:ncb79b, author = "R. Seydel", title = "Numerical computation of branch points in ordinary differential equations", journal = "Numer. Math.", year = "1979", volume = "32", pages = "51--68", annote = "bifurcation, numerical analysis", } @Article{seydel:ncp81, author = "R. Seydel", title = "Numerical computation of periodic orbits that bifurcate from stationary solutions of ordinary differential equations", journal = "Appl. Math. Comput.", year = "1981", volume = "9", pages = "257--271", annote = "bifurcation, numerical analysis", } @Article{seydel:bsb83, author = "R. Seydel", title = "Branch switching in bifurcation problems for ordinary differential equations", journal = "Numer. Math.", year = "1983", volume = "41", pages = "93--116", annote = "bifurcation, numerical analysis", } @Article{sherrat:mab91, author = "J. A. Sherrat and J. D. Murray", title = "Mathematical analysis of a basis model for epidermal wound healing", journal = "J. Math. Biol.", year = "1991", volume = "29", pages = "389--404", annote = "Bio", } @Article{sherrat:mew90, author = "J. A. Sherrat and J. D. Murray", title = "Models of epidermal wound healing", journal = "Proc. R. Soc. Lond. B", year = "1990", volume = "241", pages = "29--36", annote = "Bio", } @Article{siegberg:shr81, author = "H. Siegberg", title = "Some historical remarks concerning degree theory", journal = "Amer. Math. Monthly", year = "1981", volume = "88", pages = "125--139", } @Article{simpson:mnd75, author = "R. B. Simpson", title = "A method for the numerical determination of bifurcation states of nonlinear systems of equations", journal = "SIAM J. Numer. Anal.", year = "1975", volume = "12", number = "3", pages = "439--451", annote = "bifurcation, numerical analysis", } @Article{singer:sob78, author = "D. Singer", title = "Stable Orbits and Bifurcations of Maps of the Interval", journal = "SIAM J. Appl. Math.", year = "1978", volume = "35", number = "2", month = sep, pages = "260--267", annote = "BIF", } @Article{stakgold:bsn71, author = "I. Stakgold", title = "Branching solutions of nonlinear equations", journal = Srev, year = "1971", volume = "13", pages = "289--332", annote = "BIF", } @Article{stefan:tse77, author = "P. Stefan", title = "A theorem of {S}arkovskii on the existence of periodic orbits of continuous endomorphisms of the real line", journal = "Comm. Math. Phys.", year = "1977", volume = "54", pages = "237--248", annote = "1D maps", } @Article{straffin:ppc78, author = "Jr. Straffin and D. Phillip", title = "Periodic Points of Continuous Functions", journal = "Mathematics Magazine", year = "1978", volume = "51", number = "2", month = mar, pages = "99--105", } @Article{sweers:sep89, author = "G. Sweers", title = "Semilinear elliptic problems on domains with corners", journal = "Comm. in PDE", year = "1989", volume = "14", number = "8 \& 9", pages = "1229--1247", annote = "PDE", } % % article-t % @Article{takac:abs92, author = "P. {Tak\'{a}\v{c}}", title = "Asymptotic behavior of strongly monotone time - periodic dynamical processes with symmetry", journal = "JDE", year = "1992", volume = "100", pages = "355--378", } @Article{turner:tcm75, author = "R. E. L. Turner", title = "Transversality and cone maps", journal = "Arch. Rat. Mech. Anal.", year = "1975", volume = "58", number = "58", pages = "151--179", } % % article-u % % % article-v % @Article{vorst:bfs92, author = "H. A. van der Vorst", title = "{BI-CGSTAB}: A fast and smoothly converging variant of {BI-CG} for the solution of nonsymmetric linear systems", journal = "SIAM J. Sci. Stat. Comput.", year = "1992", volume = "13", number = "2", pages = "631--644", annote = "nonsymmetric linear" } @Article{vorst:via91, author = "R. C. A. M. van der Vorst", title = "Variational identities and applications to differential systems", journal = "Arch. Rational Mech. Anal.", year = "1991", volume = "116", number = "4", pages = "375--398", annote = "pohozaev", } % % article-w % @Article{weber:nsh80, author = "H. Weber", title = "Numerical solution of {H}opf bifurcation problems", journal = "Math. Meth. in the Appl. Sc.", year = "1980", volume = "2", pages = "178--190", annote = "Hopf bifurcation, numerical analysis", } @Article{wolpert:pip81, author = "L. Wolpert", title = "Positional information and pattern formation", journal = "Phil. Trans. R. Soc. Lond.", year = "1981", volume = "295", pages = "441--450", annote = "Bio", } @Article{whitley:dds83, author = "D. Whitley", title = "Discrete dynamical systems in dimensions one and two", journal = "Bull. London Math. Soc.", year = "1983", volume = "15", pages = "177--217", annote = "1D maps", } % % article-y % @Article{yorke:pti75, author = "J. A. Yorke and T. Y. Li", title = "Period three implies chaos", journal = "Amer. Math. Monthly", year = "1975", volume = "82", pages = "985--992", annote = "1D maps", } % % article-x % @Article{xie:spb91, author = "Wenzheng Xie", title = "A sharp pointwise bound for functions with ${L}^2$-Laplacians and zero boundary values on arbitrary three dimensional domains", journal = "Indiana Univ. Math. Jour.", year = "1991", volume = "40", number = "4", pages = "1185--1192", annote = "sobolev", } %%% %%% Unpublished %%% @Unpublished{, author = "", title = "", note = "", OPTyear = "", OPTmonth = "", OPTkeyword = "", OPTannote = "" } @Unpublished{carl:etw92, author = "S. Carl", title = "An envelope theorem for weak solutions of quasilinear elliptic boundary value problems", note = "preprint", } @Unpublished{doedel:nac88, author = "E. J. Doedel", title = "Numerical {A}nalysis and {C}ontrol of {B}ifurcation {P}roblems", note = "Course Notes", year = "1988", month = dec, annote = "numerical bifurcation", } @Unpublished{doedel:scp86, author = "E. J. Doedel and J. P. Kernevez", title = "Software for continuation problems in ordinary differential equations with applications", year = "1985", note = "preprint", annote = "numerical analysis, bifurcation", } %%% an example of a citation in a latex doc: %%% ~\cite{amann:fpe76,schmitt:bvp78,lions:eps82} %%% an example of the bib build command: %%%\newpage %%%\bibliography{/u/ma/mcgough/tex/main} %%%\bibliographystyle{plain}