Based On Critical Point Theory Of Impulsive Differential Systems, Existence Of Solutions To The Problem

The research of impulsive differential systems begins in the 1960s, which not only has greatly developed in mathematics but also has involed in many other fields, such as physical and chemical technology, the dynamic analysis of the population, biological technology and economics. Therefore, the research of impulsive differential systems have vital theoretical significance and practical value. This dissertation constructs an functional, and judges the existence of critical point by using critical theory,thus obtains the sufficient condition of existence of solutions for several kinds of impulsive differential system.The dissertation includes five chapters which is summarized as follows:In chapter 1, we introduce the background, the current research situations and developments of impulsive differential systems at home and abroad, and simply introduce the mainly aspects of this dissertation.In chapter 2, we introduce some prepare knowledges of the critical point theory, and some basic definitions and theorems which are quoted by the following chapters.In chapter 3, we study for the existence of solutions for a class of second order impulsive Hamiltonian system boundary value problems,using the critical point theory and saddle point theorem. We construct an functional, and judge the existence of critical point, thus obtains the sufficient condition of the existence of solutions for this system, which has impulsive effects. Finally, some specific examples are given to verify the effectiveness of the results.In chapter 4, we study for a class of linear and nonlinear Sturm-Liouville boundary value problems of the impulsive differential system, using critical point theory,saddle point theorem and Lax-Milgram theorem, and then give the sufficient condition of existence of the solution for this boundary value problems. Finally, some specific examples are given to verify the feasibility of the results.In chapter 5, we make a summary for this article, and prospect the future development of this topic.