Skip to main content
SpringerLink
Log in

Periodic solutions of a nonlinear wave equation without assumption of monotonicity

  • Published:
Mathematische Annalen Aims and scope Submit manuscript

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.

References

  1. Amann, H., Zehnder, E.: Multiple periodic solutions for a class of nonlinear autonomous wave equations. Houston J. Math.7, 147–174 (1981)

    Google Scholar 

  2. Brézis, H.: Periodic solutions of nonlinear vibrating strings and duality principles. Proceedings AMS Symposium on the Mathematical Heritage of H. Poincaré. Bloomington, April 1980

  3. Brézis, H., Coron, J.M.: Periodic solutions of nonlinear wave equations and Hamiltonian systems. Am. J. Math.103, 559–570 (1981)

    Google Scholar 

  4. 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, 667–689 (1980)

    Google Scholar 

  5. Brézis, H., Nirenberg, L.: Forced vibrations for a nonlinear wave equation. Comm. Pure Appl. Math.31, 1–30 (1978)

    Google Scholar 

  6. Brézis, H., Nirenberg, L.: Characterizations of the ranges of some nonlinear operators and applications to boundary value problems. Ann. Scuola Norm. Sup. Pisa5, 225–326 (1978)

    Google Scholar 

  7. Dunford, N., Schwartz, J.T.: Linear operators, Vol. 1. New York: Interscience 1964

    Google Scholar 

  8. Fadell, E.R., Rabinowitz, P.H.: Generalized cohomological index theories for the group actions with an application to bifurcation questions for Hamiltonian systems. Invent. Math.45, 139–174 (1978)

    Google Scholar 

  9. Hofer, H.: On the range of wave operator with nonmonotone nonlinearity. Math. Nachr.106, 327–340 (1982)

    Google Scholar 

  10. Marlin, J.A.: Periodic motions of coupled simple pendulums with periodic disturbances. Int. J. Nonlinear Mech.3, 439–447 (1968)

    Google Scholar 

  11. Mawhin, J.: Une généralisation du théoréme de J.A. Marlin. Int. J. Nonlinear Mech.5, 335–339 (1970)

    Google Scholar 

  12. Rabinowitz, P.H.: Free vibrations for a semilinear wave equation. Comm. Pure Appl. Math.31, 31–68 (1968)

    Google Scholar 

  13. Rabinowitz, P.H.: Periodic solutions of large norm of Hamiltonian systems (to appear)

  14. Willem, M.: Densité de l'image de la différence de deux opérateurs. C.R. Acad. Sci. Paris290, 881–883 (1980)

    Google Scholar 

  15. Stedry, M., Vejvoda, O.: Existence of classical periodic solutions of a wave equation: a connection of number-theoretical character of the period with geometrical properties of solutions. Differential Equations (1983) (to appear) (in Russian)

  16. Vejvoda, O.: Partial differential equations. Noordhoff: Sijthoff 1981

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. CAI, ENSMP, 35, rue Saint-Honoré, F-77305, Fontainebleau, Cédex, France

    J. M. Coron

Authors
  1. J. M. Coron
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Coron, J.M. Periodic solutions of a nonlinear wave equation without assumption of monotonicity. Math. Ann. 262, 273–285 (1983). https://doi.org/10.1007/BF01455317

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01455317

Keywords

Search

Navigation