%0 Journal Article
%J Duke Math. J. 134 (2006) 359-419
%D 2006
%T Cantor families of periodic solutions for completely resonant nonlinear wave equations
%A Massimiliano Berti
%A Philippe Bolle
%X We prove the existence of small amplitude, $2\\\\pi \\\\slash \\\\om$-periodic in time solutions of completely resonant nonlinear wave equations with Dirichlet boundary conditions, for any frequency $ \\\\om $ belonging to a Cantor-like set of positive measure and for a new set of nonlinearities. The proof relies on a suitable Lyapunov-Schmidt decomposition and a variant of the Nash-Moser Implicit Function Theorem. In spite of the complete resonance of the equation we show that we can still reduce the problem to a {\\\\it finite} dimensional bifurcation equation. Moreover, a new simple approach for the inversion of the linearized operators required by the Nash-Moser scheme is developed. It allows to deal also with nonlinearities which are not odd and with finite spatial regularity.
%B Duke Math. J. 134 (2006) 359-419
%G en_US
%U http://hdl.handle.net/1963/2161
%1 2083
%2 Mathematics
%3 Functional Analysis and Applications
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-02T09:53:35Z\\nNo. of bitstreams: 1\\n0410618v1.pdf: 427752 bytes, checksum: 08750b5fadd830fbe76aa48d54824f17 (MD5)
%R 10.1215/S0012-7094-06-13424-5