Existence and asymptotic stability of time periodic solutions to the generalized double dispersion equation with periodic external force

Abstract

In this paper, we investigate the generalized double dispersion equation with periodic external force in Rn. We prove the existence and uniqueness of time periodic solutions that have the same period as the external force in some suitable function space for the space dimension n≥3. The proof is based on the spectral analysis for the solution operator and the contraction mapping theorem. In addition, we also discuss the time asymptotic stability of the time periodic solutions by continuous argument.