Nontrivial Solutions Of Multi-point Boundary Value Problems For Nonlinear Ordinary Differential Equations

The present thesis discusses the existence of nontrivial solutions for two classes of multi-point boundary value problems for second order nonlinear ordinary differentialequations mainly by using of the topological degree theory and fixed point index theory, which the nonlinear term can change sign, and gets some new results. The thesis is divided into three chapters.In Chapter 1, we introduce the historical background of problems which will be investigated and state the main results of this thesis. In addition,we list some preliminary knowledge which is needed in this thesis..In Chapter 2, mainly by topological degree theory and some analysis technique, we discuss the existence of nontrivial solution for singular three-point boundary value problemsFirst we give the Green's function for the corresponding problem, consider its properties,and deal with the difficulty caused by the singularity, then we establish the existence criteria for nontrivial solution, positive solution or negative solution in the condition that the nonlinear term f can change sign.Chapter 3 is concerned with four point boundary value problem for second order nonlinear ordinary differential equationand give some sufficient conditions for the single nontrivial solution or multiple nontrivial solutions. The main tools are fixed point index theory and topological degree theory.