oubly periodic solutions of a nonlinear wave equation with x-dependent coefficients

his paper is concerned with the doubly periodic solutions of the nonlinear wave equation with -dependent coefficients Such a model arises from the forced vibrations of a nonhomogeneous string and the propagation of seismic waves in nonisotropic media. Based on the properties of wave operator with -dependent coefficients, we obtain the existence of doubly periodic solutions when the nonlinearity is monotone and bounded.