Periodic Solutions And Periodic Boundary Value Problems Of Impulsive Differential Equations

This thesis of Master is composed of three chapters, which mainly studied the existence of positive periodic solutions for impulsive differential equations with de-lays, the existence of solutions for periodic boundary value problems of first-order impulsive differential equations and impulsive functional differential equations, and the existence of periodic solutions for the Duffing equation with impulses and delays.In chapter one, by using a competely continuous operator on cone and the Krasnoselskii fixed point theorem, we study the existence of positive periodic solutions of differential equations with impulses and delays, and some sufficient conditions will be given.Chapter two mainly considers the periodic boundary value problems for impul-sive differential equations. Some existence results, obtained by the help of Schaeffer's fixed point theorem and the method of upper and lower solutions coupled with the monotone iterative technique. Our main results improves and generalizes the some known results.In the last chapter, by means of the coincidence degree theory, we investigate the existence of periodic solutions for the Duffing equation with impulses and delays, and some sufficient conditions will be established, which are new even for case without impulsive point.