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 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.
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