The Research Of Second-order Three-point Impulsive Differential Equation Boundary Value Problems

On the basis of existing literatures, this dissertation discusses the existence of positive solutions for second-order impulsive differential equations three-point boundary value problems from various angles by using different fixed-point theorems. This paper is divided into four chapters, and the main contents are as follows:The introduction part introduces the research background and the current state of the research on impulsive differential equation boundary value problems, and the main contents in this paper.By using the Avery-Peterson fixed point theorem, discuss the existence of positive solutions for second-order impulsive differential equations three-point boundary value problems. By calculating the Green’s function, discussing it’s specific properties and defining the appropriate cone and operator, we obtain the existence of at least three positive solutions of this problem.For the existence of positive solutions of second-order impulsive differential equations three-point boundary value problems with sign changing nonlinearities, by using the Avery-Peterson fixed point theorem, the existence of at least two positive solutions for this problem is obtained.Discuss the existence of positive solutions for systems of second-order impulsive differential equations three-point boundary value problems by using the cone expansion and cone contraction fixed-point theorem.