With Infinite Delay Integral Differential Periodic Solution And Stability

This paper mainly discusses the periodic solutions of some integral and differential equations with infinite delay.The studies of the existence and uniqueness of the periodic solutions and the stabilities of these equations have attracted great concern in recent years and many good results have been obtained.This paper has further extended these conclusions on the foundations of them,and obtained some new results with the method of exponential dichotomy,fixed point theorem and Liapunov functional respectively.This paper has four parts.The first chapter gives the origin of the problem and some related preliminary knowledge.The second chapter discusses and proves the existence and uniqueness of periodic solutions and stability of a neutral integral and differential equation with infinite delay in detail.The third chapter discusses and proves the stability of a perturbing n-dimensional Volterra integral and differential equation. The last chapter further talks about the existence and uniqueness of the periodic solutions of a n-dimensional neutral integral and differential equation with infinite delay.