Mathematische Zeitschrift

, Volume 169, Issue 2, pp 127–166

Saddle points and multiple solutions of differential equations

  • Herbert Amann


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Amann, H., Mancini, G.: Some applications of monotone operator theory to resonance problems. J. Nonlinear Anal. (to appear)Google Scholar
  2. 2.
    Ambrosetti, A., Prodi, G.: Analisi non Lineare. Pisa: Scuola Normale Superiore de Pisa 1973Google Scholar
  3. 3.
    Ambrosetti, A., Rabinowitz, P.H.: Dual variational methods in critical point theory and applications. J. Functional Analysis14, 349–381 (1973)Google Scholar
  4. 4.
    Brezis, H., Nirenberg, L.: Characterizations of the ranges of some nonlinear operators and applications to boundary value problems. Ann. Scuola Norm. Sup. Pisa, Cl. Sci., Ser. IV,5, 225–326 (1978)Google Scholar
  5. 5.
    Brezis, H., Nirenberg, L.: Forced vibrations for a nonlinear wave equation. Comm. Pure Appl. Math.31, 1–30 (1978)Google Scholar
  6. 6.
    Castro, A.: Hammerstein integral equations with indefinite kernel. Internat. J. Math. & Math. Sci.1, 187–201 (1978)Google Scholar
  7. 7.
    Castro, A., Lazer, A.C.: Applications of a max-min principle. Rev. Colombiana Mat.10, 141–149 (1976)Google Scholar
  8. 8.
    Castro, A., Lazer, A.C.: Critical point theory and the number of solutions of a nonlinear Dirichlet problem. PreprintGoogle Scholar
  9. 9.
    Clark, D.C.: A variant of the Lusternik-Schnirelman theory. Indiana Univ. Math. J.22, 65–74 (1972)Google Scholar
  10. 10.
    Coffman, C.V.: A minimum-maximum principle for a class of nonlinear integral equations. J. Analyse Math.22, 391–419 (1969)Google Scholar
  11. 11.
    Deimling, K.: Nichtlineare Gleichungen und Abbildungsgrade. Springer Hochschultext, Berlin-Heidelberg-New York: Springer, 1974Google Scholar
  12. 12.
    Ekeland, I., Temam, R.: Analyse convexe et problèmes variationels. Paris: Dunod 1974Google Scholar
  13. 13.
    Kransnosel'skii, M.A.: Topological Methods in the Theory of Nonlinear Integral Equations. Oxford-London-New York: Pergamon Press 1964Google Scholar
  14. 14.
    Lions, J.-L., Magenes, E.: Non-Homogeneous Boundary Value Problems and Applications, I. Berlin-Heidelerg-New York: Springer 1972Google Scholar
  15. 15.
    Lovicarova, H.: Periodic solutions of a weakly nonlinear wave equation in one dimension. Czechoslowak Math. J.19, 324–342 (1969)Google Scholar
  16. 16.
    Mancini, G.: Periodic solutions of some semilinear autonomous wave equations. Boll. Un. Mat. Ital. B (5)15, 649–672 (1978)Google Scholar
  17. 17.
    Mawhin, J.: Solutions périodiques d'équations aux derivées partielles hyperbolique non linéaire. Rapport No. 84, Institut math. pure appl. Université Catholique de Louvain, 1976Google Scholar
  18. 18.
    Rabinowitz, P.H.: Periodic solutions of nonlinear hyperbolic partial differential equations. Comm. Pure Appl. Math.20, 145–205 (1967)Google Scholar
  19. 19.
    Rabinowitz, P.H.: Free vibrations for a semilinear wave equation. Comm. Pure Appl. Math.31, 31–68 (1978)Google Scholar
  20. 20.
    Rabinowitz, P.H.: Periodic solutions of Hamiltonian systems. Comm. Pure Appl. Math.31, 157–184 (1978)Google Scholar
  21. 21.
    Rabinowitz, P.H.: A variational method for finding periodic solutions of differential equations. MRC Report 1854, May 1978Google Scholar
  22. 22.
    Reed, M., Simon, B.: Methods of Modern Mathematical Physics. IV. Analysis of Operators. New York-London: Academic Press 1978Google Scholar
  23. 23.
    Rockafellar, R.T.: Monotone operators associated with saddle-functions and minimax problems. In: Nonlinear Functional Analysis. Proceedings of Symposia in Pure MathematicsXVIII, Part 1 (Chikago 1968), pp. 241–250. Providence, Rhode Island: American Mathematical Society 1970Google Scholar
  24. 24.
    Thews, K.: A reduction method for some nonlinear Dirichlet problems. J. Nonlinear Anal. (to appear)Google Scholar
  25. 25.
    Vainberg, M.M.: Variational Methods for the Study of Nonlinear Operators San Francisco: Holden Day 1964Google Scholar
  26. 26.
    Yosida, K.: Functional Analysis. Berlin-Göttingen-Heidelberg: Springer 1965Google Scholar
  27. 27.
    Berger, M.S.: Periodic solutions of second order dynamical systems and isoperimetric variational problems. Amer. J. Math.93, 1–10 (1971)Google Scholar
  28. 28.
    Clark, D.C.: On periodic solutions of autonomous Hamiltonian systems of ordinary differential equations. Proc. Amer. Math. Soc.39, 579–584 (1973)Google Scholar
  29. 29.
    Clark, D.C.: Periodic solutions of variational systems of ordinary differential equations. J. Differential Equations28, 354–368 (1978)Google Scholar
  30. 30.
    Thews, K.: Multiple solutions of elliptic boundary value problems with odd nonlinearities. Math. Z.163, 163–175 (1978)Google Scholar
  31. 31.
    Mawhin, J.: Periodic solutions of nonlinear dispersive wave equations. Rapport 120, Inst. de Math., Université Catholique de Louvain, 1978Google Scholar

Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • Herbert Amann
    • 1
  1. 1.Mathematisches Institut der UniversitätZürichSwitzerland

Personalised recommendations