%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