Periodic Solutions To Nonlinear Wave Equations With Variable Coefficients

In this paper,we mainly study the nonlinear variable coefficients wave equation system with general boundary conditions.This model describes the forced vibration of bounded inhomogeneous strings and the propagation of seismic waves in inhomogeneous media.By using Global Inverse Function Theorem,we prove the existence and uniqueness of the periodic solutions for such system.Its proof depends essentially on the properties of the spectrum of wave operators with variable coefficients.Finally,we give a priori estimate of the weak solution.