Displaying similar documents to “Lyapunov center theorem for some nonlinear PDE's : a simple proof”

Bifurcation of free vibrations for completely resonant wave equations

Massimiliano Berti, Philippe Bolle (2004)

Bollettino dell'Unione Matematica Italiana

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We prove existence of small amplitude, 2p/v-periodic in time solutions of completely resonant nonlinear wave equations with Dirichlet boundary conditions for any frequency ω 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.