Solvability For Several Kinds Of Multi-point Boundary Value Problems Of Differential Equations

This thesis of master is composed of four chapters, which mainly study the solutions for several kinds of multi-point boundary value problems of differential equations.Chapter one is an introduction of the background and actuality of the research about this object.In chapter two, by means of the Krasnoselskii fixed-point theorem, we study the existence of positive solutions for two kinds of nonlinear singluar second-order multi-point boundary value problemsandand some sufficient conditions are established. We improve some known results, and obtain some new results.Chapter three mainly considers the existence of solutions for a kind of third-ordertwo point boundary value problemBy means of the mixed monotone iterative operator and the fixed point theorem of the mixed monotone iterative operator,we study and prove the existence and uniqueness of the solution of third-order two-point boundary value problem.In the last chapter, we investigate a kind of third-order three points nonlinear differential equationsWe prove the existence of solution for the boundary value problem with the use of lower and upper solution method and Schauder fixed point theorem.The construction of lower and upper solutions are also presented.