Bifurcation of free vibrations for completely resonant wave equations

M. Berti; P. Bolle

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Bifurcation of free vibrations for completely resonant wave equations

M. Berti·P. Bolle

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Abstract

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.

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M. Berti, P. Bolle. 2004-09-03. Bifurcation of free vibrations for completely resonant wave equations. https://arxiv.org/abs/math/0409052

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