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.

中文翻译：

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具有可变波速和周期性强迫的波方程的响应解

我们考虑具有周期性变化的波速和周期性外力的非线性波动方程模型。通过在频率上施加非共振条件，我们在渐近全测度的康托尔集合中为这样的模型建立了响应解（即与强迫具有相同频率的周期解）的存在性。证明依赖于 Lyapunov-Schmidt 约简以及 Nash-Moser 迭代。