Stability And Asymptotic Behavior Of Several Impulsive Delay Differential Equations

Differential equations were originally created to study physical and astronomy problems at the end of the seventeenth century.After hundreds of years of development,Differential equations have become an important branch of mathematics.This thesis consists of five chapters,which mainly focuses on the qualitative analysis of the solutions of several kinds of impulsive delay differential equations.In chapter 1,we briefly introduces the generation of impulsive delay differential equations,our research and the main results.In chapter 2,we discuss the asymptotic properties of solutions for a class of neutral differential equations under appropriate impulsive perturbations,and prove the solutions of apporoach constant under certain conditions by using Lyapunov functional method.In chapter 3,we study the stability for a class of delay differential equations.We obtain the condition of impulsive stability and asymptotic stability,and reveal the mechanism of impulsive stability.In chapter 4,we study the asymptotic properties of solutions of neutral differential equations with constant impulse and forcing terms.We use a method different from the Lyapunov function,we obtain the sufficient condition that each oscillatory solution and non-oscillatory solution of the equation approaches zero.Finally,we summarizes the main research results and makes a prospect for the future work.