The Existence Of Positive Solutions For Two Class Of Boundary Value Problems Of Impulsive Differential Equation Systems

With the development of the times, the mathematical model for differential equations has been more widely used. Research in the field of impulsive differential equations is also increasing. On the basis of existing literatures, this dissertation discusses the existence of positive solutions for boundary value problems of impulsive differential equation systems by using Krasnoselskii fixed point theorem and Leggett-Williams fixed point theorem. This paper is divided into three chapters, and the main contents are as follows:The first chapter is the introduction part. In this part, we give an outline of introduce the research background and the current state of the research on impulsive differential equation and impulsive differential equation systems boundary value problems, and the main contents in this paper.In chapter two, we study the existence of positive solutions for periodic boundary value problems of first-order impulsive differential equation systems. Firstly, appropriate linear space and norm are defined, and appropriate operator is given. Under the certain conditions of nonlinear term and pulse value, by the Krasnoselskii fixed point theorem, we provide sufficient conditions under which the above periodic boundary problem system has at least one positive solution or at least two positive solutions. By the Leggett-Williams fixed point theorem, we provide sufficient conditions under which the above periodic boundary problem system has at least three positive solutions.In chapter three, we discuss the existence of positive solutions for boundary value problems of second-order impulsive differential equation systems. The proof of our main result is based upon transformation techniques and Krasnoselskii fixed point theorem, we provide sufficient conditions under which the above boundary problem system has at least one positive solution.