Periodic Solutions And Asymptotically Periodic Solutions For Several Kinds Of Evolution Equations

As an important branch of differential equations,evolution equations can be used to describe time varying states or processes in biology,mechanics and other natural sciences,which attracts many scholars' interest.When the actual factors such as the ecological envi-ronment and air friction are taken into consideration,the asymptotic periodic phenomenon is more consistent with the actual life than the periodic phenomenon,therefore,in recent years,many scholars have studied the properties of the periodic solutions(for differential equations)with its extend forms such as:almost periodic solution,asymptotically almost periodic solutions,asymptotically periodic solution,S-asymptotically ?-periodic solution,pseudo S-asymptotically ?-periodic solution,etc.Motivates by above,in this thesis main-ly,operator semigroup,Banach fixed point,Leray-Schauder alternative theorem and some analysis techniques are used to study the existence of periodic solutions and pseudo S-asymptotic periodic solutions for several types of evolution equations.The organization of this thesis is as follows.In Chapter 1,we briefly introduce the development and some related research back-ground of periodic solution and pseudo S-asymptotic ?-periodic solution.In Chapter 2,we use the Banach fixed point theorem and Bellman inequality to study the existence and stalbility of periodic solutions for a class of non-autonomous evo-lution equations.In Chapter 3,using operator scmigroup theory and fixed point theorem to illustrate the existence of pseudo S-asymptotically ?-periodic solutions for a class of neutral evolu-tion equations.This chapter is divided into two sections:In section 1,using operator semigroup theory and the Banach fixed point theorem to discuss the existence of the pseudo S-asymptotic ?-periodic solution under the general condition of the evolution equation.In section 2,using operator semigroup theory and the Leray-Schauder alternative theorem to get the existence and inference of the pseudo S-asymptotic ?-periodic sollution for the evolution equation.