Existence Of Solutions For Some Kinds Of Multi-point Boundary Value Problems Of Ordinary Differential Equations With P-Laplacian

The boundary value problems with p-Laplacian operator arise in a variety of applied areas such as applied mechanics, astrophysics and electricity. In this paper, we mainly study the multi-point boundary value problems for ordinary differential equation with p-Laplacian operator by using the method of upper and lower solution and Leray-Schauder degree theory.The paper consists of five chapters:In chapter 1, we mainly introduce the background, the progress of related theory for multi-point boundary value problems with p-Laplacian operator, and describe the main contents and the methods of this paper, and give some pre-knowledge, which is used in this paper.In chapter 2, we establish some existence conditions of solution for second order multi-point boundary value problems with p-Laplacian operator by using the strictly the method of upper and lower solution and the Leray-Schauder alternative theorem.In chapter 3, we construct the auxiliary equation and study the existence of at least one solution for second order Sturm-Liouville-like boundary value problems, by using the method of upper and lower solution and the homotopy invariance of Leray-Schauder degree. Then, we discuss the convergence of iterative sequence by monotone iterative techniques and the quasilinear method.In chapter 4, we obtain the existence results of solution for fourth-order multi-point boundary value problems with p-Laplacian operator by using the upper and lower solution method and the homotopy invariance of Leray-Schauder degree.In chapter 5, we mainly summarize the paper and prospect for future work.