 02468 Massimiliano Berti, Philippe Bolle
 Periodic solutions of
nonlinear wave equations with general nonlinearities
(565K, PS)
Nov 18, 02

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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 LyapunovSchmidt reduction and
variational arguments.
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