μ-Pseudo Almost Automorphic Solutions To Two Classes Of Evolution Equations

In this article, we mainly discuss some basic properties of Stepanov-like μ pseudo almost automorphic functions and the existence of μ-pseudo almost automorphic mild solutions to two classes of semilinear evolution differential equations. This thesis are divided into four sections.In section 1, we introduce the research backgrounds and the main results of this thesis.Besides a series of recent theoretical achievements to the theory of μ-pseudo almost automorphic functions, Stepanov-like μ-pseudo almost automorphic functions in abstract spaces.Section 2 is preliminaries, we will list certain knowledge that will be used throughout this thesis. This part mainly include some basic definitions, notations, theorems, lemmas, methods and properties about almost automorphic functions, pseudo almost automorphic functions,μ-ergodic functions,μ-pseudo almost automorphic functions,Stepanov-like μ-pseudo almost automorphic functions. In addition, we introduce briefly the definitions and related notations of uniformly exponentially stable and strongly continuous family of operators.Next, in Section 3 we are focused on discussing the existence and uniqueness to of μ-pseudo almost automorphic mild solutions to semilinear integro-differential equation:In the last Section 4, we mainly discuss the existence and uniqueness of μ-pseudo almost automorphic mild solutions to semilinear integral equation in the form listed below...