Response solutions for wave equations with variable wave speed and periodic forcing

Abstract

We consider a model of nonlinear wave equations with periodically varying wave speed and periodic external forcing. By imposing non-resonance conditions on the frequency, we establish the existence of the response solutions (i.e., periodic solutions with the same frequency as the forcing) for such a model in a Cantor set of asymptotically full measure. The proof relies on a Lyapunov--Schmidt reduction together with the Nash--Moser iteration.