Positive Solutions Of Singular Boundary Value Problem

By using the knowledge of nonlinear functional analysis such as fixed point index theorem and perturbation technique etc., we study the positive solutions of singulary boundary value problem. This thesis include the following three contents.Chapter 1 present two sufficient conditions which guarantee the existence and uniqueness of positive solution for a class of SBVP (Sturm-Liouville SBVP). At the same time, we also gain a sufficient and necessary condition of the same problem.In chapter 2, we investigate the existence of multiple positive solutions for third-order three-point semipositone SBVP under supperlinear or sublinear conditions.Considering the essential difference between finite and infinite dimensional space, in chapter 3 we add some compactness type conditions and discuss the existence of multiple positive solutions for a class of SBVP of integro-differential equations in Banach space.