Bifurcation of free vibrations for completely resonant wave equations

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We prove existence of small amplitude, 2 pi/omega -periodic in time solutions of completely resonant nonlinear wave equations with Dirichlet boundary conditions for any frequency omega belonging to a Cantor-like set of positive measure and for a generic set of nonlinearities. The proof relies on a suitable Lyapunov-Schmidt decomposition and a variant of the Nash-Moser Implicit Function Theorem.
7 pages

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Analysis of PDEs, 53L05, 37K50, 58E05

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http://salesiana.dossiersoluciones.com/handle/123456789/72359

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0409052
 http://arxiv.org/abs/math/0409052

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arXiv