Research On The Existence Of Positive Solutions Of Boundary Value Problems For A Kind Of P-Laplacian Equation And Equations

This paper mainly researches on the existence of positive solutions of boundary value problems for a kind of second order differential equations and singular p-Laplacian equation and n-dimension p-Laplacian equations. This article is divided into four chapters:The first chapter outlines the problem of the historical background and the main results of the present stage, outlines the main work of this paper.Chapterâ…¡, by using Krasnosel'skii fixed point theorem, it mainly researches on the existence of one positive solution of boundary value problems for second order differential equations.Chapterâ…¢, by using Leggett-Williams theorem, it mainly researches on the existence of three positive solutions for boundary value problem of one kind of p-Laplacian equation and also give the sufficient conditions of the existence of three positive solutions.Chapter IV, by using fixed point index theorem, it mainly establishes the existence theorem of one positive solution and two positive solutions of three-point singular boundary value problems for n-dimensional p-Laplacian.