01284nas a2200145 4500008004100000022001300041245008900054210006900143300001400212490000800226520074600234100002400980700002001004856011401024 2008 eng d a0001870800aCantor families of periodic solutions for wave equations via a variational principle0 aCantor families of periodic solutions for wave equations via a v a1671-17270 v2173 aWe 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.1 aBerti, Massimiliano1 aBolle, Philippe uhttps://www.math.sissa.it/publication/cantor-families-periodic-solutions-wave-equations-variational-principle