Massimiliano Berti, Philippe Bolle
Bifurcation of free vibrations
for completely resonant wave equations
(30K, Latex)

ABSTRACT.  We prove existence of small amplitude,   
$2\pi \slash \om$-periodic in time solutions of completely resonant 
nonlinear wave equations for any frequency $ \om $ 
belonging to a Cantor-like set of positive measure. 
The proof relies on a suitable Lyapunov-Schmidt decomposition 
and a variant of the Nash-Moser Implicit Function Theorem.