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arXiv · 1711.09437

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

Bochao Chen·Yixian Gao·Yong Li·Xue Yang
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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.

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Bochao Chen, Yixian Gao, Yong Li, Xue Yang. 2017-11-26. Response solutions for wave equations with variable wave speed and periodic forcing. https://arxiv.org/abs/1711.09437

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