Skip to main content
SpringerLink
Log in

Forced vibrations of superquadratic Hamiltonian systems

  • Published:
Acta Mathematica

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Adams, R. A.,Sobolev spaces. Academic Press, New York (1975).

    MATH  Google Scholar 

  2. Amann, H., Multiple periodic solutions of autonomous Hamiltonian systems. InRecent contributions to nonlinear partial differential equations H. Berestycki & H. Brezis editors. Pitman, London (1981).

    Google Scholar 

  3. Amann, H. &Zehnder, E., Nontrivial solutions for a class of nonresonance problems and applications.Ann. Scuola Norm. Sup. Pisa (4), 7 (1980), 593–603.

    MathSciNet  Google Scholar 

  4. Bahri, A.,Thèse de Doctorat d’Etat. Univ. P. et M. Curie, Paris, 1981.

  5. Bahri, A. Groupes d’homotopie des ensembles de niveau pour certaines fonctionnelles à gradient Fredholm. To appear.

  6. Bahri, A., Résultats topologiques sur une certaine classe de fonctionnelles et applications à l’étude de certains problèmes elliptiques sur-linéaires.J. Funct. Anal. To appear.

  7. Bahri, A. &Berestycki, H., A perturbation method in critical point theory and applications.Trans. Amer. Math. Soc., 267 (1981), 1–32.

    Article  MATH  MathSciNet  Google Scholar 

  8. —, Points critiques de perturbations de fonctionnelles paires et applications.C. R. Acad. Sci. Paris. Sér. A, 291 (1980), 189–192.

    MATH  MathSciNet  Google Scholar 

  9. —, Existence d’une infinité de solutions périodiques de certains systèmes hamiltoniens en présence d’un terme de contrainte.C. R. Acad. Sci. Paris Sér. A 292 (1981), 315–318.

    MATH  MathSciNet  Google Scholar 

  10. Bahri, A. & Berestycki, H., Existence of forced oscillations for some nonlinear differential equations.Comm. Pure Appl. Math. To appear.

  11. Benci, V., To appear.

  12. Benci, V., A geometrical index for the groupsS 1 and some applications to the research of periodic solutions of O.D.E.’s. To appear.

  13. Benci, V., On the critical point theory for indefinite functionals in the presence of symmetries.Trans. Amer. Math. Soc., To appear.

  14. Benci, V. &Rabinowitz, P. H., Critical point theorems for indefinite functionals.Invent. Math., 52 (1979), 241–273.

    Article  MATH  MathSciNet  Google Scholar 

  15. Brézis, H., Coron, J. M. &Nirenberg, L., Free vibrations for a nonlinear wave equation and a theorem of P. Rabinowitz.Comm. Pure Appl. Math., 33 (1980), 667–689.

    MATH  MathSciNet  Google Scholar 

  16. Clarke, F. H. & Ekeland, I., Nonlinear oscillations and boundary value problems for Hamiltonian systems. To appear.

  17. Conner, E. E. &Floyd, F., Fixed point free involutions and equivariant maps.Bull. Amer. Math. Soc., 66 (1960), 416–441.

    Article  MATH  MathSciNet  Google Scholar 

  18. Ekeland, I., Periodic solutions of Hamiltonian equations and a theorem of P. Rabinowitz.J. Differential Equations, 34 (1979), 523–534.

    Article  MATH  MathSciNet  Google Scholar 

  19. Ekeland, I., Forced oscillations de systèmes Hamiltoniens non linéaires, III.Bull. Soc. Math. France. To appear.

  20. Ekeland, I. Oscillations de systèmes Hamiltoniens non linéaires, III.Bull. Soc. Math. France. To appear.

  21. Fadell, E., Husseini, S. & Rabinowitz, P. H., OnS 1 versions, of the Borsuk-Ulam Theorem. To appear.

  22. Fadell, E. &Rabinowitz, P. H., Generalized cohomological index theories for Lie group action with an application to bifurcation questions for Hamiltonian systems.Invent. Math., 45 (1978), 134–174.

    Article  MathSciNet  Google Scholar 

  23. Fučik, S.,Solvability of nonlinear equations and boundary value problems. D. Reidel, Boston (1980).

    MATH  Google Scholar 

  24. Krasnosel’skii, M. A.,Topological methods in the theory of nonlinear integral equations. MacMillan, New York (1964).

    Google Scholar 

  25. Lions, J. L. &Magenes, E.,Problèmes aux limites non homogènes et applications, vol. 1. Dunod, Paris (1968).

    MATH  Google Scholar 

  26. Marino, A. &Prodi, G., Metodi perturbativi nella teoria di Morse.Boll. Un. Mat. Ital., 11 (1975), 1–32.

    MATH  MathSciNet  Google Scholar 

  27. Nirenberg, L., Comments on nonlinear problems.Proceeding of a conference in Catania (Italy), September 1981. To appear.

  28. Rabinowitz, P. H., Free vibrations for a semi-linear wave equation.Comm. Pure Appl. Math., 31 (1978), 31–68.

    MATH  MathSciNet  Google Scholar 

  29. —, Periodic solutions of Hamiltonian systems.Comm. Pure Appl. Math., 31 (1978), 157–184.

    MathSciNet  Google Scholar 

  30. —, A variational method for finding periodic solutions of differential equations. InNonlinear evolution equations. M. G. Crandall Ed., pp. 225–251. Academic Press, New York (1968).

    Google Scholar 

  31. —, On subharmonic solutions of Hamiltonian systems.Comm. Pure Appl. Math., 33 (1980), 609–633.

    MATH  MathSciNet  Google Scholar 

  32. Rabinowitz, P. H., Variational methods for nonlinear eigenvalue problems. InEigenvalues of nonlinear problems. Roma (1974), Ediz. Cremonese.

  33. Rabinowitz, P. H., On large norm periodic solutions of some differential equations. To appear.

  34. Schwartz, J. T.,Nonlinear functional analysis. Gordon & Breach, New York (1969).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Chicago, Chicago, IL, USA

    A. Bahri & H. Berestycki

  2. Université Pierre et Marie Curie, Paris Cedex, France

    A. Bahri & H. Berestycki

Authors
  1. A. Bahri
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. H. Berestycki
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The work of the second author has been supported in part by NSF Grant MCS-8104242.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bahri, A., Berestycki, H. Forced vibrations of superquadratic Hamiltonian systems. Acta Math 152, 143–197 (1984). https://doi.org/10.1007/BF02392196

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02392196

Keywords

Search

Navigation