Existence And Multiplicity Of Solutions For Several Classes Of Impulsive Differential Equations

Impulsive differential equation is widely used in physics,biology,medicine and other fields,and has a strong practical background and research value.In this thesis,the existence and multiplicity of solutions of three impulsive differential equations are studied by means of variational method and critical point theory.In other words,a functional is defined in an appropriate function space,so that the critical point corresponding to the functional is the solution of the impulsive differential equation,and then the existence and multiplicity of solutions are studied through the critical point theory.The specific content consists of six chapters,which are summarized as follows:In chapter 1,the research background and significance of impulsive differential equations are introduced,and the research status of different types of impulsive differential equations at home and abroad is briefly described.The research status of three kinds of boundary value problems of impulsive differential equations related to the research of this thesis is mainly introduced,and the main work and innovation of this thesis are introduced.In chapter 2,some basic definitions involved in this thesis and the critical point theory needed in the process of proof are introduced.In chapter 3,the boundary value problem of second order non-instantaneous impulsive differential equations is discussed.By using variational method and critical point theory,it is concluded that there is at least two weak solutions.In chapter 4,the three-point boundary value problem of p-Laplacian differential equations with instantaneous and non-instantaneous impulses is discussed.By using variational method and critical point theory,it is conclude that there is at least one classical solution to this problem.In chapter 5,the boundary value problem of second order impulsive differential equation coupled systems is discussed.By using variational method and critical point theory,it is concluded that there is at least one classical solution and at least two classical solutions for the system.Concrete examples are given to illustrate the applicability of the main results.The last chapter,we summarize the current research work and put forward some followup research ideas.