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.