Multiple Positive Solutions To Singular Three-point Boundary Value Problems For The One-Dimension P-Laplacian

Singular boundary value problems for nonlinear ordinary differential equations, is become an impotant topic in ordinary equations fields.This thesis is composed of two chapters. In the first chapter, we introduce the historical background of problems which will be investigated and the main results of this paper. In Chapter 2, we establish the existence of multiple positive solutions for the singular nonlinear boundary value problemby using the Leray-Schauder alternative and the fixed point theorem in cones, whereΦ(s) = |s|^p-2s, p > 1. The singularity may appear at u = 0 and t = 0.In [6,7](p = 2), R. P. Agarwal and D. O'Regan used Leray-Shauder alternative and the fixed point theorem in cones to establish the existence of two positive solutions when q(t) may be singular at t = 0 or t = 1, nonlinearity may be singular at y = 0.The purpose of this paper is to establish the existence of multiple positive solutions of problem by applying the method as used in [6, 7].