Existence Of Positive Solutions For Two Kinds Of Differential Equations Of Boundary Value Problems With P-Laplacian

Boundary value problems have been one of the important lessons of the theoretical and applied research of differential equations. To some extent, boundary value problems with p-Laplacian operator are more important than ordinary boundary value problems. This paper is concerned with boundary value problems for differential equations and delay differential equations with p-Laplacian operator, respectively. The existence of positive solutions is given by using Avery-Peterson fixed point theorem and Schauder fixed point theorem, respectively. This paper is divided in three parts.The first chapter briefly introduces the background, development and preliminaries of differential equations with p-Laplacian, and concludes the main conclusions.In the second chapter, a class of third-order three-point boundary value problems with p-Laplacian operator is considered. A new nonlinear operator is built, verified whether it is completely continuous, and transformed the operator fixed point problem. Sufficient conditions for the existence of three positive solutions are obtained by using Avery-Peterson fixed point theorem.Chapter3is concerned with three-point boundary value problems of fourth-order delay differential equations with p-Laplacian operator. At least, one positive solution is obtained by using Schauder fixed point theorem. Two examples are given to illustrate the availability of main results.