The existence and uniqueness of almost periodic and asymptotically almost periodic solutions of semilinear Cauchy inclusions

Abstract

The main aim of this paper is to investigate almost periodicity and asymptotic almost periodicity of abstract semilinear Cauchy inclusions of first order with (asymptotically) Stepanov almost periodic coefficients. To achieve our goal, we employ fixed point theorems and the well known results on the generation of infinitely differentiable degenerate semigroups with removable singularites at zero.