Positive Solutions Of Singular Second Order Nonlinear Boundary Value Problems

The present paper employs the cone theory, fixed point index theory, and Krasnoselskii fixed point theorem and so on, to investigate the existence of solutions to boundary value problem of several kinds of nonlinear systems of differential equations. The thesis is divided into three sections according to contents.In chapter 1, we consider the existence of positive solutions for the following singular super-linear boundary value problemswhere f(t,x)∈((0,∞)×(0,∞), [0,+∞)), f(t, 1) (?) 0, t∈(0,∞).In Chapter 2, we investigate the existence of positive solutions for boundary value problemwhere f : C(0,1)×[0, +∞)→[0, +∞) is continous and f may be singular at t = 0,1.In Chapter 3, we investigate the positive solutions of the problemwhere f : (0,+∞)→[0,+∞) is continuous, h : [0,1]→[0, +∞) is also continuous and h(x) (?) 0.