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

Yu Fei,Yongkun Li

doi:10.3390/math10030435

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.

Highlights

It is worth mentioning that Reference [7] studies the existence of 1-almost automorphic solutions in the sense of Besicovitch for a class of first-order nonautonomous linear differential equations
It is very meaningful to study the composition theorem of almost automorphic functions in the sense of Besicovitch and the existence of almost automorphic solutions in the sense of Besicovitch of nonlinear differential equations
The rest of this paper is arranged as follows: in Section 2, we study some basic properties of almost automorphic functions in the sense of Besicovitch

Summary

Introduction

It is worth mentioning that Reference [7] studies the existence of 1-almost automorphic solutions in the sense of Besicovitch for a class of first-order nonautonomous linear differential equations. It is very meaningful to study the composition theorem of almost automorphic functions in the sense of Besicovitch and the existence of almost automorphic solutions in the sense of Besicovitch of nonlinear differential equations. The rest of this paper is arranged as follows: in Section 2, we study some basic properties of almost automorphic functions in the sense of Besicovitch.

Besicovitch Almost Automorphic Functions and Their Some Properties

Besicovitch Almost Automorphic Solutions of Equation 1

An Example

Conclusions