- 02-468 Massimiliano Berti, Philippe Bolle
- Periodic solutions of
nonlinear wave equations with general nonlinearities
Nov 18, 02
(auto. generated ps),
of related papers
Abstract. We prove the existence of
small amplitude periodic solutions, with strongly irrational
frequency $ \om $ close to one, for completely resonant
nonlinear wave equations.
We provide multiplicity results
for both monotone and nonmonotone nonlinearities.
For $ \om $ close to one we prove the existence of a large
number $ N_\om $ of
$ 2 \pi \slash \om $-periodic in time solutions
$ u_1, \ldots, u_n, \ldots, u_N $:
$ N_\om \to + \infty $ as $ \om \to 1 $.
The minimal period of the $n$-th solution $u_n $ is proved to be
$2 \pi \slash n \om $.
The proofs are based on a Lyapunov-Schmidt reduction and