Massera Type Criteria For Some Classes Of Evolution Equations

There exist various of periodic phenomenon in the real world. So it is very interesting and improtant problem to study differential equations modelling these phenomena.The existence of periodic solutions and the boundedness of solution are two important topics in the theory of differential equations. This was first considered by J.Massera in his landmark paper[l]. A classical result of Massera in this paper says that a linear periodic differential equation is a necessary and sufficient condition on the existence of periodic solutions is that it has a bounded solution on the positive half line. Recently, many authors have devoted themselves to the study Massera type theorem, and there has been an increasing interest in extending this classical result to various classes of equations.In this paper, our main interest is to study Massera type theorems for the existence of periodic solutions of five classes of evolution equations. We will review these results and present some new progress in the research of periodic solutions of some classes of evolution equations. And some of these results improve or extend the related results in the literatures.This dissertation is consist of five sections. In Section 1, we consider an...