TY - JOUR
T1 - Cantor families of periodic solutions for wave equations via a variational principle
JF - Advances in Mathematics
Y1 - 2008
A1 - Massimiliano Berti
A1 - Philippe Bolle
AB - We prove existence of small amplitude periodic solutions of completely resonant wave equations with frequencies in a Cantor set of asymptotically full measure, via a variational principle. A Lyapunov-Schmidt decomposition reduces the problem to a finite dimensional bifurcation equation-variational in nature-defined on a Cantor set of non-resonant parameters. The Cantor gaps are due to "small divisors" phenomena. To solve the bifurcation equation we develop a suitable variational method. In particular, we do not require the typical "Arnold non-degeneracy condition" of the known theory on the nonlinear terms. As a consequence our existence results hold for new generic sets of nonlinearities. © 2007 Elsevier Inc. All rights reserved.
VL - 217
N1 - cited By (since 1996)6
ER -