Types Of Ordinary Differential Equations Point Boundary Value Problems Study

This thesis is devoted to multiple-point boundary value problem of ordinary differential equation. It consists of five chapters.In chapter one, we summarize the historical background and current conditions for the ordinary differential equation boundary value problems.In chapter two, we study existence of solutions for a kind of second order multiple-point boundary value problems. Using Avery—Peterson fixed point theorem, we obtain the conclusion that the boundary value problem has at least three positive solutions under suitable conditions.In chapter three, we study the existence of solutions for a kind of forth order multiple-point boundary value problem. Combining lower and upper solutions methods and monotone iterative techniques, we get the minimal and maximal solutions.In chapter four, we are devoted to the existence of solutions for a kind of multiple point boundary value problems with p-Laplace operator. Just like that in chapter two, using Avery—Peterson fixed point boundary value problem, we obtain the conclusion that the boundary value problem has at least three positive solutions under suitable conditions.In chapter five, we use monotone iterative method to study the boundary value problem in chapter four and obtain that this boundary value problem has at least one positive solution under suitable conditions. Unlike chapter four, we give a solution series which converges to the terminal solution.In chapter six, we use new fixed- point theorem to study the problems in chapter two and obtain sufficient conditions for the existence of three positive solutions of that boundary value problems.