Existence Of Positive Solutions Of Multi-point Boundary Value Problems For Non-linear Ifferential Equations

Recently, third-order boundary value problems for ordinary differential equations have received much attention, Many authors have made a series of studies, the main tools are the fixed point theorems and the upper and lower solution method. This thesis consists of four chapters,which mainly investigated the existence of positive solutions of three-pointboundary value problems for nonlinear differential equations.In chapter 1 we introduce the historical background of problems which will be investigatedstate the main results of this thesis. In addition, we list some preliminary knowledge which is needed later.In chapter 2 we study the existence of positive solutions of the following three-order three-point boundary value problems for nonlinear differential equationsand establish some suficient conditions for the existence of single, twin and three positivesolutions by using nonlinear alternative of Leray-Schauder type, Guo-Krasnoselskii's fixed point theorem and Leggett-Williams fixed point theorem.Chapter 3 is concerned with the following three-order three-point boundary value problemsthe existence of one and two Positive Solutions.In chapter 4 we deal with the following nonlinear boundary value problem with parameter. The nonexistence, existence and multiplicity of positive solutions are obtained by means of fixed-point index theory on the cone. In particular, our results extend and improve some relate conclusions in recent literatures.