Study On A Class Of Sturm-Liouville Boudary Value Problems

In this thesis, we study mainly the existence of positive solutions of a class of Sturm-Liouville boundary value problems for second order singular nonlinear ordinary differential equations, by using the fixed point theorems in the cone theory . The paper is divided into three chapters, the content is the following :Chapter one is an introduction, first, it introduces briefly the background of generating nonlinear ordinary differential equation boundary value problems(BVP) and the methods and meanings of research on the BVP; then it summarizes the research situation of nonlinear ordinary differential equation boundary value problems in recent years, and research problems of the paper; finally , it mainly introduces the fundamental concepts as required , also it presents a fixed point theorem often applied in the paper by means of fixed point index in the cone theory and related results.In Chapter two , we study the existence of positive solutions of a class of second order singular nonlinear Sturm-Liouville two-point boundary value problems under a new condition and show the existence of at least two positive solutions for this Sturm-Liouville boundary value problems .In Chapter three , we investigate the existence of positive solutions of second order singular nonlinear Sturm-Liouville multi-point boundary value problems and obtain the existence of at least two positive solutions for this class of second order singular Sturm-Liouville multi-point boundary value problems in which the nonlinear terms satisfy some new kind conditions.