Existence And Multiplicity Of Positive Solutions Of Boundary Vaule Problems Of Differential Equations

This thesis is concerned with the existence and multiplicity of positive solutions of boundary value problems for several classes of differential equations. The thesis contains five chapters.In chapter 1, the backgrounds of boundary value problems of differential equations, theorems for fixed points and main results are given.Boundary value problems of second, third order ordinary differential equations are considered in chapter 2,3, respectively. By using properties of Green functions, original problems are transferred into integral equations. By resorting to fixed point theorems, the existence and multiplicity of positive solutions are obtained under the suitable conditions.In chapter 4, the existence of positive solutions of the singular boundary value problems of functional differential equations with p-Laplacian is discussed. Under the suitable conditions, the existence of three positive solutions is established by using an abstract fixed point theorem.In Chapter 5,we are concerned with the existence and multiplicity of symmetric positive solutions for the second-order three-point boundary value proble. By using Leggett-Williams, fixed point theorem, we provide sufficient conditions for the existence of at least three positive solutions to the problems.