Several Singular Nonlinear Boundary Value Problems Of Positive Solutions

In this paper, we use the cone theory, the fixed point theory, the fixed point index theory to study several kinds of boundary problems for nonlinear singular differential equation.The thesis is divided into four chapters according to contents.In chapter 1, we generally introduce the center opinion of the paper.In chapter 2, we use Krasnoselkii-Guo fixed point theorem to investigate the symmetric positive solutions of a class of singular two point boundary value problems for nonlinear differential equations in Banach spaces, where a> 0,β≥0 is a constant, p∈C([0,1],[0,+∞)),p(t)> 0,t∈(0,1) and p(t)= p(1-t),t∈[0,1]. the nonlinear term f may be singular with two variables. we obtain the existence of positive symmetric solutions for boundary value problem (2.1.1).In chapter 3, we use the fixed point theory and the fixed index theory to investigate the following singular three point boundary value problem with sign changing nonlinearity whereα∈[0,1/2],η∈(0,1) is a constant, a(t)∈C[0,1],f∈C((0,1)×[0,+∞), R).we obtain the existence of positive symmetric solutions for boundary value problem (3.1.1).In chapter 4, we use the cone theorem and the fixed point theorem to inves-tigate the existence of multiple monotone positive solutions for a class of singular boundary value problem with p-Laplacian: where We prove that there exist at least two monotone positive solutions for boundary value problem (4.1.1).