Study Of The Existence Of Positive Solutions For Second-Order Impulsive Differential Systems

In this paper,we study the existence and multiplicity of positive solutions for three kinds of second-order impulsive differential systems with indefinite weight.The full text is divided into the following five chapters.In Chapter 1,the background and the overseas and domestic research status of two-point boundary value problems,nonlocal boundary value problems,impulsive differential equations and indefinite weight problems are introduced,and the main contents of this paper is also included.Finally,some basic concepts and theorems are given.In Chapter 2,we investigate the existence and multiplicity of positive solutions for second-order impulsive differential equation with indefinite weight.By using the fixed point theorem of cone expansion and compression of norm type,we obtain existence result of at least one positive solution and three positive solutions.In Chapter 3,we study the second-order impulsive differential systems with indefinite weight and muti-parameter.Applying Krasnoselskii's fixed point theorem in a cone,we establish solvable intervals of parameters to guarantee the second-order impulsive differential boundary value problem admits at least two positive solutions.And we give an example to verify the main results.In Chapter 4,we investigate the existence and multiplicity of positive solutions for second-order nonlocal indefinite impulsive differential systems.By constructing a cone K,which is the Cartesian product of two cones K1×K2 in the space PC[0,1],and using Krasnoselskii's fixed point theorem in a cone,some new sufficient conditions for the existence of positive solutions are given,and the feasibility of the conclusion is verified by an example.In Chapter 5,we give the summary of the main conclusions of above chapters and the prospects of the research we will study.