Periodic Solutions to Nonlinear Wave Equation with X-Dependent Coefficients Under the General Boundary Conditions

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Abstract

In this paper we consider a class of nonlinear wave equations 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 proof is based on a Lyapunov–Schmidt reduction together with a differentiable Nash–Moser iteration scheme.

Keywords

Wave equations General boundary conditions Periodic solutions Lyapunov–Schmidt reduction Nash–Moser iteration 

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Authors and Affiliations

  1. 1.School of Mathematics and Statistics, Center for Mathematics and Interdisciplinary SciencesNortheast Normal UniversityChangchunPeople’s Republic of China
  2. 2.College of MathematicsJilin UniversityChangchunPeople’s Republic of China

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