Existence Of Positive Solutions For Boundary Value Problems Of Several Kinds Of Delay Differential Equation With P-laplacian

In this dissertation, by using upper and lower solutions method, Gou-Krasnosel’skii fixed-point theorem in cones and a fixed point theorem due to A very and Peterson, the existence of positive solutions for boundary value problems of delay differential equation with p-Laplacian. The dissertation consists of four chapters as follows:The fist chapter is the introduction, we give a survey to the background and history of boundary value problems of delay differential equation with p-Laplacian. The structure of this paper and the topics to be studied are briefly summarized. At the end of this chapter, We give the preliminaries that would be used in this dissertation.In chapter2, by using upper and lower solutions method and Gou-Krasnosel skii fixed-point theorem in cones, we mainly discuss the existence of positive solutions for boundary value problems of delay differential equation with p-Laplacian. we obtain sufficient conditions for the existence results of positive solutions.In chapter3. by using the Avery-Peterson fixed-point theorem on a cone, we mainly discuss multi-point boundary value problems of delay differential equation with p-Laplacian, the first order derivative appearing in nonlinear term. We obtain sufficient conditions for the existence results of three positive solutions at least.The last chapter is conclusion, we summerize the paper and propos several questions which are worth further studying.