Periodic solutions of Birkoff–Lewis type for the nonlinear wave equation

Abstract

We prove existence and multiplicity of small amplitude periodic solutions with large period for the wave equation with small ‘mass’. Such solutions bifurcate from resonant finite dimensional invariant tori of the fourth order Birkhoff normal form of the associated hamiltonian system. The number of geometrically distinct solutions and their minimal periods tend to infinity when the ‘mass’ tends to zero.