Existence Of Multiple Solutions For Boundary Value Problems Of Second Order Impulsive Differential Equations

In this dissertation,we mainly discuss the existence of multiple solutions for boundary value problems of Impulsive Differential Equations with derivative terms,which are non-singular and singular.The general idea of the study of non-singular impulsive differential equations is to transform impulsive differential equations into corresponding impulsive integral equations,and then,we obtain the existence of multiple solutions by means of different fixed point theories.It consisits of three chapters.The first chapter introduces the background and significance of the research,the research trends,the main work and some preliminary knowledge of this paper.The second chapter mainly introduces the existence of multiple solutions for boundary value problems of second-order impulsive differential equations.This chapter consisits of two parts.The first part mainly discusses the existence of two positive solutions of second-order impulsive differential equations by using the exponential fixed point theorem.With using the five-functional fixed point theory,the second part mainly studies the existence of three positive solutions of second-order impulsive differential equations.Two examples verifies the results.In Chapter 3,we discuss the existence of multiple solutions for boundary value problems of Second Order Impulsive Differential Equations with singularities.First,we obtain the existence of multiple solutions of Singular Impulsive Differential equations,by constructing a special operator.Then,we use the fixed point theory of cone stretching and cone compression to test the existence of multiple solutions.Conclusivelly,an example is given to illustrate the theorem.