%0 Journal Article
%J Advances in Mathematics
%D 2008
%T Cantor families of periodic solutions for wave equations via a variational principle
%A Massimiliano Berti
%A Philippe Bolle
%X 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.
%B Advances in Mathematics
%V 217
%P 1671-1727
%G eng
%R 10.1016/j.aim.2007.11.004