Besicovitch almost periodic solutions of abstract semi-linear differential equations with delay

Abstract

In this paper, we first use the Bohr property to give a definition of Besicovitch almost periodic functions, and study some basic properties of Besicovitch almost periodic functions, including the equivalence of the Bohr property and the Bochner property. Then, as an application, we use the contraction principal to obtain the existence and uniqueness of Besicovitch almost periodic solutions for a class of abstract semi-linear differential equations with delay.