Positive Solutions For A BVP Of Third-order Differential Equation

The paper is divided into three chapters .Chapter 1 is the introduction of this paper, which introduce the history and the current situation of the boundary value problem of differential equations. We will also display some basic tools in this chapter.In chapter 2, we consider the multiple nondecreasing positive solutions for a singular nonlinear third-order three-point boundary value problem. Some existence results of multiple nondecreasing positive solutions are obtained by using the well-known Leggett-Williams fixed-point theorem.In chapter 3, we deal with a nonlinear third-order three-point boundary value problem with parameter. The nonexistence, existence and multiplicity of positive solutions are obtained by means of fixed-point index theorem on the cone.