Existence and Multiplicity of Periodic Solutions for Dirichlet–Neumann Boundary Value Problem of a Variable Coefficient Wave Equation

Abstract

Abstract In this paper, we consider the periodic solutions of a variable coefficient wave equation which models the forced vibrations of a nonhomogeneous string and the propagation of seismic waves in nonisotropic media. Under Dirichlet–Neumann boundary conditions, we find some important properties for the variable coefficient wave operator. Then, based on these properties, we obtain the existence and multiplicity of periodic solutions by using the Leray–Schauder degree theory.