Abstract
In this paper, we investigate the existence of multiple nontrivial periodic solutions for an asymptotically linear wave equation with x-dependent coefficients. Such a mathematical model can be derived from the forced vibrations of a nonhomogeneous string and propagation of seismic waves in nonisotropic media. By constructing a suitable function space, we characterize the problem as a variational problem, and then we prove that there are at least three nontrivial periodic solutions via variational methods.
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