Almost Automorphic Solutions in the Sense of Besicovitch to Nonautonomous Semilinear Evolution Equations

Abstract

In this paper, we study the existence of almost automorphic solutions in the sense of Besicovitch for a class of semilinear evolution equations. Firstly, we study some basic properties of almost automorphic functions in the sense of Besicovitch, including the composition theorem. Then, by using the Banach fixed point theorem, the existence of almost automorphic solutions in the sense of Besicovitch to the semilinear equation is obtained. Finally, we give an example of partial differential equations to illustrate the applicability of our results.