Solutions And Positive Solutions For Several Classes Of Multi-point Boundary Value Problems Of Differential Equations (Systems)

Multi-point boundary value problems(BVPs for short) of differential equations are an important branch in the theory of nonlinear analysis,which arise in different fields of applied mathematics and physic and have wide applications on elasticity and stability theory.Therefore,it is significant to study the solutions or positive solutions of multi-point BVPs.The paper is divided into four chapters:Chapter 1 is the introduction of this paper,which introduce the studying background of this thesis and our main works.In addition,we list some preliminary knowledge needed in this paper.In chapter 2,we discuss the existence of at least one positive solution to a system of singular second-order four-point BVPs by applying the functional expansioncompression fixed point theorem.In chapter 3,we concern a singular third-order m-point BVPs.Some existence criteria of at least one solution are established by using Leray-Schauder Continuation Principle.In chapter 4,we first establish a new fixed point theorem of Leggett-Williams type,and then apply the fixed point theorem to obtain the existence of three and 2n-1 monotone positive solutions of a third-order m-point BVPs.