Existence Of Multiple Positive Solutions For Several Kinds Of Impulsive Differential Equation Boundary Value Problems

In this thesis,the existence of multiple positive solutions,the continuous dependence of positive solutions on parameters and the optimal interval of positive solutions for boundary value problems of second order,fourth order and nth order impulsive differential equations is systematically studied by applying Leggett-Williams fixed point theorem,fixed point index theory,eigenvalue theory,transformation technique and H?lder's inequality.According to the research content and research methods,the full text is divided into five chapters.In Chapter 1,the background and significance of the boundary value problem of impulsive differential equations are introduced,and the main contents of this paper are put forward according to the research status at home and abroad.Finally,some basic concepts and theorems are given.In Chapter 2,we discuss a class of boundary value problem for a second-order impulsive differential equation with integral boundary conditions and a delayed argument.We first give the expression of the Green function of the corresponding homogeneous boundary value problem,and study its properties.Furthermore,applying Legget-William's fixed point theorem and H?lder's inequality,we obtain the existence results of at least three positive solutions.Finally,an example is given to illustrate our conclusion.In Chapter 3,we study the existence of multiple positive solutions for a class of fourth order impulsive differential equations and the dependence of positive solutions on the parameter.By using two transformations and fixed point theorems,the existence of positive solutions,multiple solutions and the dependence of positive solutions on the parameter of the impulsive beam equation are established.It is worth mentioning that we not only give estimates on the norms of these solutions,but also discuss the dependence of positive solutions on the parameter and in the end through an example to verify the correctness of the main results.In Chapter 4,we study the existence of positive solutions for a class of eigenvalue problems with an advanced argument.The optimal interval of the parameters l is established by using the transformation technique,the inequality and the eigenvalue theory.In this interval,we prove that there is a positive solution for the impulsive differential equation with an advanced argument.In Chapter 5,we give the main conclusions and prospects.