We prove existence of small amplitude, 2π/ω-periodic in time solutions of completely resonant nonlinear wave equations with Dirichlet boundary conditions for any frequency to 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.
Bifurcation of free vibrations for completely resonant wave equations / Berti, M.; Bolle, P.. - In: BOLLETTINO DELL'UNIONE MATEMATICA ITALIANA. B. - ISSN 0392-4041. - 7B:2(2004), pp. 519-528.
Bifurcation of free vibrations for completely resonant wave equations
Berti, M.;
2004-01-01
Abstract
We prove existence of small amplitude, 2π/ω-periodic in time solutions of completely resonant nonlinear wave equations with Dirichlet boundary conditions for any frequency to 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.File in questo prodotto:
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