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Cantor families of periodic solutions of wave equations with C k nonlinearities

  • Massimiliano BertiEmail author
  • Philippe Bolle
Article

Abstract.

We prove bifurcation of Cantor families of periodic solutions for wave equations with nonlinearities of class C k . It requires a modified Nash-Moser iteration scheme with interpolation estimates for the inverse of the linearized operators and for the composition operators.

2000 Mathematics Subject Classification:

35L05 37K50 37K55 

Keywords:

Nonlinear wave equation infinite dimensional Hamiltonian systems periodic solutions Lyapunov-Schmidt reduction small divisors Nash-Moser theorem 

Copyright information

© Birkhaueser 2008

Authors and Affiliations

  1. 1.Dipartimento di Matematica e Applicazioni, R. CaccioppoliUniversità Federico IINapoliItaly
  2. 2.Université d’Avignon et des Pays de Vaucluse, Laboratoire d’Analyse non linéaire et Géométrie (EA2151)AvignonFrance

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