A Class Of One-dimensional Singular P-laplacian Nonlinear Boundary Value Problem Of Multiple Positive Solutions,

Singular boundary value problems for nonlinear ordinary differential equations, which arise in a variety of areas such as mechanics, boundary layer theory, diffusion and reaction equations, biology, ect, become an im-potant 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-Sehauder alternative and the fixed point theorem in cones, where (s)=|s|p-2S, p>1. The singularity may appear at u = 0 and t = 0.Recently, the singular boundary value problems have been studied extensively. However, there are only few works on singular boundary value problems for One-Dimension p-Laplacian. As far as the author knows, the works on the existence of twin positive solutions to the singular boundary value problems for One-Dimension p-Laplacian are quite rarely seen.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.In [4, 5], the authors used the Krasnoselski's fixed point theorem in cones to establish the existence of multiple positive solutions when f is superlinear or sublinear. However, f is not singular at u = 0.Motivated by the results mentioned above, 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].