Positive Solutions To Bvps Of Higher Order Differential Equations

This paper investigate the existence of positive solutions to multi-point boundary value problem for several kinds of higher order differential equations.We mainly apply a Krasnoselskii’s fixed point theorem in cone and a fixed point theorem in partially ordered sets.Our results improve and extend the relevant existing of literature results.This paper of Master is composed of four chapters.In chapter1,we make it as introduction of this paper,which mainly narrate that the historical background and current situation of differential equation and the main work in this paper.In chapter2,we mainly consider the following existence and nonexistence of positive solutions for a three-point boundary value problemsBy using Krasnoselskii’s fixed point theorem in Banach spaces, we obtain sufficient conditions for existence and nonexistence of positive solutions to a three-point boundary value problems.In chapter3,we consider the following existence of positive solutions to nonlinear∞-point boundary value problemsBy using approxinmation method and fixed point theorem in cones,We show the existence of at least one positive solution if f is either superlinear or sublinear.In chapter4, we investigate the following existence and uniqueness of positive solutions to nonlinear n-order multi-point boundary value problem We mainly apply a fixed point theorem in partially ordered sets to obtain sufficient conditions for the existence and uniqueness of positive solutions.