Boundary Value Problems For Ordinary Differential Equations

Boundary value problems occur in various fields of natural science. The ex-istence of solutions for boundary value problems attracts much attention of many famous mathematicians all around the world. In this thesis, the existence of so-lutions for several classed of nonlinear differential equations boundary value prob-lems are investigated by using the fixed-point theorems (including Krasnosel’skii’s fixed-point theorem, increasing operator fixed-point theorem, Schauder fixed-point theorem). The thesis consists of four chapters.In Chapter1, we present a short background and history of researches on boundary value problems for nonlinear ordinary differential equations and the main contributions of the paper.In Chapter2, we consider the existence of solutions for a class of first-order boundary value problem on an unbounded domain with impulsive conditions. We obtain the existence conditions by means of Krasnosel’skii’s fixed-point theorem.In Chapter3, we discuss the existence of positive solutions of boundary value problem for first order differential equation. By constructing a special normal cone and using the increasing operator fixed point theorem, we present some existence results about positive solutions of boundary value problem for a class of first order differential equation.Chapter4is devoted to the existence of positive solutions of the boundary value problem for an nth-order nonlinear impulsive integro-differential equations on an infinite interval by means of Schauder fixed point.