Bifurcation of free vibrations for completely resonant wave equations

2004/09/03 by M. Berti, Berti, M., P. Bolle +1
Mathematics · #37K50 #53L05 #58E05 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:37K50 #msc:53L05 #msc:58E05

paper · pdf · doi:10.48550/arxiv.math/0409052

7 pages

arxiv created 2004/09/03 · arxiv updated 2009/12/01

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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