The Stability Of Solution, Periodic Solution And Periodic Boundary Value Problems Of Degenerate, Impulsive Differential Equation With Delay

In many practical fields, degenerate and impulsive phenomena exist extensively, such as engineering, economy, biology, and so on. And this phenomenon has attracted many scholars' attention and lots of available and important results have been obtained.However,delay is a common phenomenon in the objective world and engineering fields. We notice that, in many practical systems, in order to describle the system more accurately, we must take the influence of either degenerate and delay or impulse and delay into consideration altogether.So, it has a practical significance to study the character of solutions of either degenerate differential system with delay or impulsive differential equations with delays.This thesis mainly discusses the stability of solutions of degenerate differential system with delay , periodic solutions and periodic boundary value problems of differential equations with impulses and delays. It is composed of four chapters, which mainly study the stability of solutions of a kind of degenerate differential system with delay, the existence of positive periodic solutions for impulsive differential equations with delays, and the existence of positive solutions for periodic boundary value problems of first-order impulsive functional differential equations.In chapter one,the backgrounds and significance of the problems are given. The main work done in this paper is introduced.In chapter two, we discuss the stability of the solutions of a kind of degenerate differential system with delay when index is 1. We give a concrete Liapunov functional and a corresponding theorem.