Periodic Solutions to Nonlinear Wave equation with $X$-dependent Coefficients under the General Boundary Conditions

Bochao Chen; Yong Li; Xue Yang

Periodic Solutions to Nonlinear Wave equation with $X$-dependent Coefficients under the General Boundary Conditions

Dynamical Systems 2017-06-14 v1

Authors: Bochao Chen , Yong Li , Xue Yang

Abstract

In this paper we consider a class of nonlinear wave equation with $x$ -dependent coefficients and prove existence of families of time-periodic solutions under the general boundary conditions. Such a model arises from the forced vibrations of a nonhomogeneous string and the propagation of seismic waves in nonisotropic media. The proofs are based on a Lyapunov-Schmidt reduction together with a differentiable Nash-Moser iteration scheme.

Keywords

nonlinear wave equation periodic solutions Lyapunov-Schmidt reduction Nash-Moser iteration general boundary conditions

Cite

@article{arxiv.1706.03921,
  title  = {Periodic Solutions to Nonlinear Wave equation with $X$-dependent Coefficients under the General Boundary Conditions},
  author = {Bochao Chen and Yong Li and Xue Yang},
  journal= {arXiv preprint arXiv:1706.03921},
  year   = {2017}
}