Existence Of Solutions For A Kind Of Boundary Value Problems Of Differential Equations

This paper mainly investgates the existence of periodic solutions of a kind of ordinary differential equtions with p-Laplacian oporator and positive solutions of a class of fourth-order m-point boundary value problems by using topological degree theory and cone theory. The main contens are as follows:In chapter 1, we give some definitions and fixed point theorems .which will be crutial in next chapters.In chapter 2, by using topological degree theory and some analytical skill, some criteria to guarantee the existence of T-periodic solutions are derived for p-Laplacian equation with a deviating argument of the following formIn chapter 3, we consider the existence of positive solutions for the following fourth order m-point boudrary value problem:where (?) We show that it has at least one or two positive solutions under some assumptions by applying Krasnoselskii's fixed point theorem and fixed point index theory.Chapter 4 is mainly about the summarization of this paper and the prospect of the future work.