Massimiliano Berti, Philippe Bolle
Periodic solutions of 
nonlinear wave equations with general nonlinearities
(565K, PS)

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 
variational arguments.