The Existence Of Positive Solutions For Singular Boundary Value Problems With One-Dimensional P-Laplacian

Nonlinear functional analysis is an important branch of modern analysis. It arouse the attention of more and more mathematicans since it can deal with all kinds of nonlinear problems in reality. The nonlinear singular boundary value problems with one-dimensional p-laplacian comes from applied mathematics and physics and is now one of the most active research field in modern analysis. In this thesis, using the variational method, cone theory and Leggett-Williams theorem, we consider the existence problem of positive solutions of nonlinear singular boundary value problem of one-dimensional p-laplacian and get some new results in this field.This thesis is composed of four sections.In chapter 1, we discuss the existence of positive solutions for a singular boundary value problems with p-Laplacianwhere the ruction f(t, u) may be singular at t = 0,1.In Chapter 2, by using a fixed point theorem in cones, the sufficient conditions of the existence of one or multiple positive solutions for singular boundary value problemsare obtained.In Chapter 3, we discuss the existence of positive solutions for a class of singular boundary value problems of functional differential equations with p-LaplacianBy using a fixed point theorem in cones, the sufficient conditions of the existence of one or multiple positive solutions for singular boundary value problems of functional differential equations are given.In Chapter 4, by using Leggett-Williams theorem, we establish the existence of three positive solutions for the singular nonlinear problems with p-Laplacianwhereφ(s) = |s|^p-2s, p> 1.