Research On Triple Positive Solutions For A Multi-point Boundary Value Problem With A One-dimensional P-Laplacian

With the rapid development of the differential equation, its applications are constantly updated. Over the years, differential equation has become a significant tool for scientific analysis and problem solving in recent decades. Qualitative study of solution of differential equations boundary value problem is currently a hot issue. More than ten years, development of nonlinear functional analysis provides a powerful support to this issue. This thesis mainly discusses the existence of multiple positive solutions for p-Laplacian differential equationwith Sturm-Liouville boundary conditions. I chose the proper cone to use Avery-Peterson fixed point theorem getting existence of three positive solutions with the boundary value problem under some given condition. Full text is divided into three chapters, main content as follows:The first chapter is the introduction section. At first, the paper introduced the background of differential equation with multiple point boundary value problems, and then wrote something about development process of boundary value problems in recent years. At last, it focused on some significant conclusion of ordinary differential equations with multiple point boundary value problems.On chapter two, the paper mainly introduced Avery-Peterson fixed point theorem and some related knowledge.The last chapter, I gave triple positive solutions for a multi-point boundary value problem with a one-dimensional p-Laplacian theorem.