Skip to main content
Log in

Twenty years of ordinary differential equations through twelve Oberwolfach meetings

  • Published:
Results in Mathematics Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. H. Amann, Gewöhnliche Differentialgleichungen, de Gruyter, Berlin, 1983

    Google Scholar 

  2. A.A. Andronov, F.A. Leontovich, I.I. Gordon and A.G. Meyer, Theory of bifurcations of dynamical systems on a plane, Wiley, New York, 1973

    Google Scholar 

  3. V.I. Arnold, Equations différentielles ordinaires, Mir, Moscou, 1974

    MATH  Google Scholar 

  4. V.I. Arnold, Geometrical methods in the theory of ordinary differential equations, Springer, New York, 1983

    Book  MATH  Google Scholar 

  5. V.I. Arnold, Méthodes mathématiques de la mécanique classique, Mir, Moscou, 1976

    MATH  Google Scholar 

  6. D.V. Anosov, A.I. Arnold, S.P. Novikov, Ya.G. Sinai (eds), Dynamical systems, vol. I to VI, Springer, Berlin, 1988–1991

    MATH  Google Scholar 

  7. J.P. Aubin, Viability Theory, 1990

  8. J.P. Aubin and A. Cellina, Differential inclusions, Springer, New York, 1964

    Google Scholar 

  9. J.P. Aubin and I. Ekeland, Applied nonlinear analysis, Wiley, New York, 1984

    MATH  Google Scholar 

  10. B. Aulbach, Continuous and discrete dynamics near manifolds of equilibria, Springer, Berlin, 1984

    MATH  Google Scholar 

  11. E.A. Barbashin, Introduction to the theory of stability, Wolters-Noordhoff, Groningen, 1970

    MATH  Google Scholar 

  12. V. Barbu, Nonlinear semigroups and differential equations in Banach spaces, Noordhoff, Leyden, 1976

    Book  MATH  Google Scholar 

  13. T. Bedford and J. Swift (eds), New directions in dynamical systems, Cambridge Univ. Press, Cambridge, 1988

    MATH  Google Scholar 

  14. M.S. Berger, Nonlinearity and functional analysis, Academic Press, New York, 1977

    MATH  Google Scholar 

  15. M.S. Berger and M. Berger, Perspectives in nonlinearity, Benjamin, New York, 1968

    MATH  Google Scholar 

  16. S.R. Bernfeld and V. Lakshmikantham, An introduction to nonlinear boundary value problems, Academic Press, New York, 1974

    MATH  Google Scholar 

  17. N. Bhatia and G.P. Szegö, Stability of dynamical systems, Springer, Berlin, 1970

    Book  MATH  Google Scholar 

  18. Yu.N. Bibikov, Local theory of nonlinear analytic ordinary differential equations, Springer, Berlin, 1979

    MATH  Google Scholar 

  19. J. Blot, Systèmes hamiltoniens: leurs solutions périodiques, Cedic, Paris, 1982

    MATH  Google Scholar 

  20. N.N. Bogoliubov, Yu.A. Mitropolsky and A.M. Samoilenko, Methods of accelerated convergence in nonlinear mechanics, Springer, Berlin, 1976

    Book  Google Scholar 

  21. R. Bowen, On axiom A diffeomorphisms, Amer. Math. Soc., Providence, 1978

    MATH  Google Scholar 

  22. J. Carr, Applications of center manifold theory, Springer, New York, 1981

    Book  Google Scholar 

  23. L. Cesari, Asymptotic behavior and stability problems in ordinary differential equations, Springer, Berlin, third edition 1971

    Book  MATH  Google Scholar 

  24. K.C. Chang, Infinite dimensional Morse theory and its applications, Sémin. Math. Sup., Univ. Montréal, Montréal, 1985

    MATH  Google Scholar 

  25. K. Chang and F. Howes, Nonlinear singular perturbation phenomena, Springer, New York, 1984

    Book  MATH  Google Scholar 

  26. P.R. Chernoff and J.E Marsden, Properties of infinite dimensional Hamiltonian systems, Springer, Berlin, 1974

    MATH  Google Scholar 

  27. S.N. Chow and J.K. Hale, Methods of bifurcation theory, Springer, New York, 1982

    Book  MATH  Google Scholar 

  28. Ch. Conley, Isolated invariant sets and the Morse index, Amer. Math. Soc., Providence, 1978

    MATH  Google Scholar 

  29. P. Constantin, C. Foias, B. Nicolaenko and R. Temam, Integral manifolds and inertial manifolds for dissipative partial differential equations, Springer, New York, 1989

    Book  MATH  Google Scholar 

  30. R. Conti, Linear differential equations and control, Academic Press, London, 1976

    MATH  Google Scholar 

  31. W.A. Coppel, Disconjugacy, Springer, Berlin, 1971

    MATH  Google Scholar 

  32. W.A. Coppel, Dichotomies in stability theory, Springer, Berlin, 1978

    MATH  Google Scholar 

  33. C. Corduneanu, Integral equations and stability of feedback systems, Academic Press, New York, 1973

    MATH  Google Scholar 

  34. J. Cronin, Differential equations, Dekker, New York, 1980

    MATH  Google Scholar 

  35. J.L. Dalecskii and M.G. Krein, Stability of solutions of differential equations in Banach spaces, Amer. Math. Soc., Providence, 1974

    Google Scholar 

  36. D.G. De Figueiredo, The Ekeland variational principle with applications and detours, Tata Institute, Bombay, 1989

    MATH  Google Scholar 

  37. K. Deimling, Ordinary differential equations in Banach spaces, Springer, Berlin, 1977

    MATH  Google Scholar 

  38. K. Deimling, Nonlinear functional analysis, Springer, Berlin, 1985

    Book  MATH  Google Scholar 

  39. R.L. Devaney, An introduction to chaotic dynamical systems, Benjamin, Menlo Park, 1986

    MATH  Google Scholar 

  40. J. Dugundji and A. Granas, Fixed point theory, PWN, Warsaw, 1982

    MATH  Google Scholar 

  41. M.S.P. Eastham, The spectral theory of periodic differential equations, Scottisch Academic Press, Edinburgh, 1973

    MATH  Google Scholar 

  42. W. Eckhaus, Asymptotic analysis of singular perturbation, North-Holland, Amsterdam, 1979

    Google Scholar 

  43. J. Eckmann and D. Ruelle, Ergodic theory of chaos and strange attractors, Institut Hautes Etudes Scient., Bures-sur-Yvette, 1985

    Google Scholar 

  44. I. Ekeland, Convexity methods in Hamiltonian mechanics, Springer, Berlin, 1990

    Book  MATH  Google Scholar 

  45. B. Fiedler, Global bifurcation of periodic solutions with symmetry, Springer, Berlin, 1988

    MATH  Google Scholar 

  46. P. Fife, Mathematical aspects of reacting and diffusing systems, Springer, Berlin, 1979

    Book  MATH  Google Scholar 

  47. A.M. Fink, Almost periodic differential equations, Springer, Berlin, 1974

    MATH  Google Scholar 

  48. H.I. Freedman, Deterministic mathematical models in population ecology, HIFR Cons., Edmonton, 1980

    MATH  Google Scholar 

  49. S. Fučik, Solvability of nonlinear equations and boundary value problems, Reidel, Dordrecht, 1980

    MATH  Google Scholar 

  50. S. Fučik and A. Kufner, Nonlinear differential equations, Elsevier, Amsterdam, 1980

    MATH  Google Scholar 

  51. R.E. Gaines and J. Mawhin, Coincidence degree and nonlinear differential equations, Springer, Berlin, 1977

    MATH  Google Scholar 

  52. M. Golubitsky and D.G. Schaeffer, Singularities and groups in bifurcation theory, vol. 1 and 2 (with I. Stewart), Springer, New York, 1985, 1988

    MATH  Google Scholar 

  53. J. Grasman, Asymptotic methods for relaxation oscillations and applications, Springer, New York, 1987

    Book  MATH  Google Scholar 

  54. E.A. Grebenikov and Yu. A. Ryabov, Constructive methods in the analysis of nonlinear systems, Mir, Moscow, 1983

    MATH  Google Scholar 

  55. J. Guckenheimer and Ph. Holmes, Nonlinear oscillations, dynamical systems, and bifurcations of vector fields, Springer, New York, 1983

    MATH  Google Scholar 

  56. R.B. Guenther, Problèmes aux limites non-linéaires pour certaines classes d’équations différentielles ordinaires, Sémin. Math. Supér., Univ. Montréal, Montréal, 1985

    MATH  Google Scholar 

  57. K.P. Hadeler, Mathematik für Biologen, Springer, Berlin, 1974

    Book  MATH  Google Scholar 

  58. J.K. Hale, Ordinary differential equations, Wiley, New York, 1969

    MATH  Google Scholar 

  59. J.K. Hale, Theory of functional differential equations, Springer, New York, 1977

    Book  MATH  Google Scholar 

  60. J.K. Hale, Topics in dynamic bifurcation theory, Amer. Math. Soc., Providence, 1981

    MATH  Google Scholar 

  61. J.K. Hale, Asymptotic behavior of dissipative systems, American Math. Soc., Providence, 1988

    MATH  Google Scholar 

  62. J.K. Hale (ed.), Studies in ordinary differential equations, Math. Assoc. America, Washington, 1977

    MATH  Google Scholar 

  63. J.K. Hale, L. Magalhaes and W. Oliva, An introduction to infinite dimensional dynamical systems — geometric theory, Springer, New York, 1984

    Book  MATH  Google Scholar 

  64. A. Haraux, Nonlinear evolution equations — Global behavior of solutions, Springer, Berlin, 1981

    MATH  Google Scholar 

  65. D. Henry, Geometric theory of semilinear parabolic equations, Springer, Berlin, 1981

    MATH  Google Scholar 

  66. E. Hille, Ordinary differential equations in the complex domain, Wiley, New York, 1976

    MATH  Google Scholar 

  67. M.W. Hirsch, C. Pugh and M. Shub, Invariant manifolds, Springer, Berlin, 1977

    MATH  Google Scholar 

  68. M.W. Hirsch and S. Smale, Differential equations, dynamical systems and linear algebra, Academic Press, New York, 1974

    MATH  Google Scholar 

  69. J. Hofbauer and K. Sigmund, The theory of evolution and dynamical systems, Cambridge Univ. Press, Cambridge, 1988

    MATH  Google Scholar 

  70. F. Hoppenstaedt, Mathematical theories of population, SIAM, Philadelphia, 1975

    Google Scholar 

  71. G. Iooss, Bifurcation of maps and applications, North Holland, Amsterdam, 1979

    MATH  Google Scholar 

  72. G. Iooss and D. Joseph, Elementary stability and bifurcation theory, Springer, New York, 1980

    Book  MATH  Google Scholar 

  73. M. Irwin, Smooth dynamical systems, Academic Press, New York, 1980

    MATH  Google Scholar 

  74. K. Jörgens and J. Weidmann, Spectral properties of Hamiltonian operators, Springer, Berlin, 1973

    MATH  Google Scholar 

  75. W.B. Jurkat, Meromorphe Differentialgleichungen, Springer, Berlin, 1988

    Google Scholar 

  76. R.M. Kauffman, T.T. Read and A. Zettl, The deficiency index problem for powers of ordinary differntial expressions, Springer, Berlin, 1977

    Google Scholar 

  77. U. Kirchgraber and E. Stiefel, Methoden der analytischen Störungsrechnung und ihre Anwendungen, Teubner, Stuttgart, 1978

    Book  MATH  Google Scholar 

  78. U. Kirchgraber and H.O. Walther (eds), Dynamics reported, vol. 1 and 2, Teubner and Wiley, Stuttgart and London, 1988, 1989

    MATH  Google Scholar 

  79. H.W. Knobloch and F. Kappel, Gewöhnliche Differentialgleichungen, Teubner, Stuttgart, 1974

    Book  MATH  Google Scholar 

  80. M.A. Krasnosel’skii, The operator of translation along trajectories of ordinary differential equations, Amer. Math. Soc., Providence, 1968

    Google Scholar 

  81. M.A. Krasnosel’skii, V.S. Burd and Yu.S. Kolesov, Nonlinear almost periodic oscillations, Wiley, New York, 1973

    Google Scholar 

  82. M.A. Krasnosel’skii and P.P. Zabreiko, Geometric methods of nonlinear analysis, Springer, Berlin, 1984

    Book  Google Scholar 

  83. S.G. Krein, Linear differential equations in Banach spaces, Amer. Math. Soc., Providence, 1971

    Google Scholar 

  84. J. Kurzweil, Ordinary differential equations, Elsevier, Amsterdam, 1986

    MATH  Google Scholar 

  85. G.E. Ladas and V. Lakshmikantham, Differential equations in abstract spaces, Academic Près, New York, 1972 [86] V. Lakshmikantham and S. Leela, Differential and integral inequalities, theory and applications, Academic Press, New York, 1969

    Google Scholar 

  86. J.P. LaSalle, Stability theory and invariance principles, SIAM, Philadelphia, 1977

    Google Scholar 

  87. H. Leipholtz, Stability theory, Academic press, New York, 1970

    Google Scholar 

  88. B.M. Levitan and V.V. Zhikov, Almost periodic functions and differential equations, Cambridge Univ. Press, Cambridge, 1982

    MATH  Google Scholar 

  89. N.G. Lloyd, Degree theory, Cambridge Univ. Press, Cambridge, 1978

    MATH  Google Scholar 

  90. W. Magnus and S. Winkler, Hill’s equation, Dover, New York, 1979

    Google Scholar 

  91. L. Markus, Lectures in differentiabe dynamics, Revised edition, Amer. Math. Soc., Providence, 1980

    Google Scholar 

  92. R.H. Martin, Nonlinear operators and differential equations in Banach spaces, Wiley, New York, 1976

    MATH  Google Scholar 

  93. D.I. Martyniuk, Lectures on the theory of stability of solutions of systems with retardations, Kiev, 1971

  94. M. Matsuda, First order algebraic differential equations, Springer, Berlin, 1980

    Book  MATH  Google Scholar 

  95. J. Mawhin, Topological degree methods in nonlinear boundary value problems, Amer. Math. Soc., Providence, 1979

    MATH  Google Scholar 

  96. J. Mawhin, Compacité, monotonie et convexité dans létude des problèmes aux limites semilinéaires, Sémin. analyse moderne, Univ. de Sherbrooke, Sherbrooke, 1981

    Google Scholar 

  97. J. Mawhin, Points fixes, points critiques et problèmes aux limites, Sémin. Math. Supér., Univ. Montréal, Montréal, 1985

    MATH  Google Scholar 

  98. J. Mawhin, Problèmes de Dirichlet variationnels non linéaires, Sémin. Math. Supér., Univ. Montréal, Montréal, 1987

    MATH  Google Scholar 

  99. J. Mawhin and M. Willem, Critical point theory and Hamiltonian systems, Springer, New York, 1989

    Book  MATH  Google Scholar 

  100. R.M. May, Stability and complexity in model ecosystems, Princeton Univ. Press, Princeton, 1973

    Google Scholar 

  101. R. Mc Kelvey (ed.), Lectures on ordinary differential equations, Academic Press, New York, 1970

    Google Scholar 

  102. R. Miller, Nonlinear Volterra integral equations, Benjamin, Menlo Park, 1971

    MATH  Google Scholar 

  103. A.B. Mingarelli, Volterra-Stieltjes integral equations and generalized ordinary differential expressions, Springer, Berlin, 1983

    MATH  Google Scholar 

  104. A.B. Mingarelli and S.G. Halvorsen, Non-oscillation domains of differential equations with two parameters, Springer, Berlin, 1988

    MATH  Google Scholar 

  105. J. Moser, Lectures on Hamiltonian systems, Amer. Math. Soc., Providence, 1968

    Google Scholar 

  106. J. Moser, Stable and random motions in dynamical systems, Princeton Univ. Press, Princeton, 1973

    MATH  Google Scholar 

  107. E. Müller-Pfeiffer, Spectral theory of ordinary differential operators, Ellis Horwood, Chichester, 1981

    MATH  Google Scholar 

  108. J. Murray, Lectures on nonlinear differential equation models in biology, Clarendon, Oxford, 1977

    Google Scholar 

  109. V.V. Nemitskii, M.M. Vainberg and R.S. Gusarova, Operational differential equations, in “Progress in Math.”, vol. 1, Plenum Press, New York, 1968

    Google Scholar 

  110. A.C. Newell, Soliton mathematics, Sémin. Math. Supér., Univ. Montréal, Montréal, 1986

    MATH  Google Scholar 

  111. S.B. Norkin, Differential equations of the second order with retarded arguments, Amer. Math. Soc., Providence, 1972

    Google Scholar 

  112. R.D. Nussbaum, The fixed point index and some applications, Sémin. Math. Supér., Univ. Montréal, Montréal, 1985

    MATH  Google Scholar 

  113. J. Palis and W. de Melo, Geometric theory of dynamical systems, Springer, New York, 1980

    Google Scholar 

  114. L. Perko, Differential equations and dynamical systems, Springer, New York, 1991

    Book  MATH  Google Scholar 

  115. L.C. Piccinini, G. Stampacchia and G. Vidossich, Ordinary differential equations, Springer, New York, 1984

    MATH  Google Scholar 

  116. V.A. Pliss, Integral manifolds of periodic systems of differential equations, Nauka, Moscow, 1977

    Google Scholar 

  117. P.H. Rabinowitz, Théorie du degré topologique et applications à des problèmes aux limites non linéaires, Univ. Paris, Paris, 1975

    Google Scholar 

  118. P.H. Rabinowitz, Minimax methods in critical point theory with applications to differential equations, Amer. Math. Soc., Providence, 1986

    Google Scholar 

  119. W.T. Reid, Sturmian theory for ordinary differential equations, Springer, New York, 1980

    Book  MATH  Google Scholar 

  120. R. Reissig, G. Sansone and R. Conti, Nichtlineare Differentialgleichungen höherer Ordnung, Cremonese, Roma, 1969

    MATH  Google Scholar 

  121. M. Roseau, Solutions périodiques ou presque périodiques des systèmes différentiels de la mécanique non linéaire, CISM Lectures, Udine, 1970

    Google Scholar 

  122. M. Roseau, Equations différentielles, Masson, Paris, 1976

    MATH  Google Scholar 

  123. F. Rothe, Global solutions of reaction diffusion systems, Springer, Berlin, 1984

    MATH  Google Scholar 

  124. N. Rouche, P. Habets and M. Laloy, Stability theory by Liapunov’s direct method, Springer, New York, 1977

    Book  MATH  Google Scholar 

  125. N. Rouche and J. Mawhin, Ordinary differential equations. Stability and periodic solutions, Pitman, Boston, 1980

    MATH  Google Scholar 

  126. D. Ruelle, Elements of differentiable dynamics and bifurcation theory, Academic Press, New York, 1989

    MATH  Google Scholar 

  127. D. Ruelle, Chaotic evolution and strange attractors, Cambridge Univ. Press, Cambridge, 1989

    Book  MATH  Google Scholar 

  128. K.P. Rybakowski, The homotopy index and partial differential equations, Springer, Berlin, 1987

    Book  MATH  Google Scholar 

  129. J.A. Sanders and F. Verhulst, Averaging methods in nonlinear dynamical systems, Springer, New York, 1985

    Book  MATH  Google Scholar 

  130. S.H. Saperstone, Semidynamical systems in infinite dimensional spaces, Springer, New York, 1981

    Book  MATH  Google Scholar 

  131. D. Sattinger, Group theoretic methods in bifurcation theory, Springer, Berlin, 1979

    MATH  Google Scholar 

  132. D. Sattinger, Branching in the presence of symmetry, SIAM, Philadelphia, 1983

    Book  Google Scholar 

  133. R. Schaaf, Global solution branches of two point boundary value problems, Springer, Berlin, 1990

    MATH  Google Scholar 

  134. S. Schwabik, Generalized differential equations, 2 volumes, Academia, Praha, 1985, 1989

    Google Scholar 

  135. S. Schwabik, M. Tvrdy and O. Vejvoda, Differential and integral equations, Academia, Praha, 1979

    MATH  Google Scholar 

  136. M.B. Sevryuk, Reversible systems, Springer, Berlin, 1986

    MATH  Google Scholar 

  137. G. Sell, Lectures on topological dynamics and differential equations, Van Nostrand, Princeton, 1971

    Google Scholar 

  138. M. Shub, Global stability of dynamical systems, Springer, New York, 1987

    Book  MATH  Google Scholar 

  139. Y. Sibuya, Global theory of a second order linear ordinary differential equation with a polynomial coefficient, North Holland, Amsterdam, 1975

    MATH  Google Scholar 

  140. C.L. Siegel and J. Moser, Lectures on celestial mechanics, Springer, New York, 1971

    Book  MATH  Google Scholar 

  141. J. Smoller, Shock waves and reaction diffusion equations, Springer, New York, 1983

    Book  MATH  Google Scholar 

  142. C. Sparrow, The Lorenz equation: bifurcation, chaos and strange attractor, Springer, New York, 1982

    Book  Google Scholar 

  143. M. Struwe, Variational methods, Springer, Berlin, 1990

    Book  MATH  Google Scholar 

  144. C.A. Swanson, Comparaison and oscillation theory of linear differential equations, Academic Press, New York, 1968

    Google Scholar 

  145. R. Temam, Infinite dimensional dynamical systems in mechanics and physics, Springer, New York, 1989

    Google Scholar 

  146. M.M. Vainberg and V.A. Trenogin, Theory of branching of solutions of non-linear equations, Noordhoff, Leyden, 1974

    MATH  Google Scholar 

  147. A. Vanderbauwhede, Local bifurcation theory and symmetry, Pitmann, London, 1981

    Google Scholar 

  148. J.C. van der Meer, The Hamiltonian Hopf bifurcation, Springer, Berlin, 1985

    MATH  Google Scholar 

  149. W. Walter, Differential and integral inequalities, Springer, Berlin, 1970

    Book  MATH  Google Scholar 

  150. W. Walter, Gewöhnliche Differentialgleichungen, Springer, Berlin, 1990

    MATH  Google Scholar 

  151. P. Waltman, Deterministic threshold models in the theory of epidemics, Springer, Berlin, 1974

    Book  MATH  Google Scholar 

  152. P. Waltman, Competition models in population biology, SIAM, Philadelphia, 1983

    Book  Google Scholar 

  153. J. Weidmann, Spectral theory of ordinary differential equations, Springer, Berlin, 1987

    Google Scholar 

  154. S. Wiggins, Global bifurcation and chaos, Springer, New York, 1988

    Book  Google Scholar 

  155. S. Wiggins, Introduction to applied nonlinear dynamical systems and chaos, Springer, New York, 1990

    Book  MATH  Google Scholar 

  156. V.A. Yakubovitch and V.M. Starzhinskii, Linear differential equations with periodic coefficients, 2 volumes, Wiley, New York, 1975

    Google Scholar 

  157. Ye Yanqian, Theory of limit cycles, Amer. Math. Society, Providence, 1986

    MATH  Google Scholar 

  158. T. Yoshizawa, Stability theory and the existence of periodic solutions and almost periodic solutions, Springer, New York, 1975

    Book  MATH  Google Scholar 

  159. E. Zeidler, Nonlinear functional analysis and its applications, 4 volumes, Springer, New York, 1986–1989

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Dedicated to H. W. Knobloch on the occasion of his 65th birthday

Work based upon a lecture given at the 1991 conference on Gewöhnliche Differentialgleichungen in Oberwolfach and realized when the author was visiting Würzburg Universität as von Humboldt Preisträger

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mawhin, J. Twenty years of ordinary differential equations through twelve Oberwolfach meetings. Results. Math. 21, 165–189 (1992). https://doi.org/10.1007/BF03323077

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03323077

Keywords

Navigation