三阶边值问题的3个正解的存在性  

Exsitence of Three Positive Solutions for Third-order Boundary Value Problem

作　　者：张立新[1] 

机构地区：[1]北京联合大学基础部,北京100101

出　　处：《四川师范大学学报（自然科学版）》2011年第4期466-470,共5页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(10671012)资助项目

摘　　要：三阶微分方程起源于应用数学、物理学等不同学科领域中,有着广泛的应用背景和重要的理论作用.考虑三阶三点边值问题,证明了线性边值问题有唯一解且其解用格林函数表示,当非线性项f满足一定增长条件时,利用Avery-Peterson不动点定理得到了上述边值问题至少有3个正解的存在性结果.Third-order differential equations arise in a variety of different areas of applied mathematics and physics,also have comprehensively applied background and important meaning of theory-oriented.This paper is concerned with the third-order three-point boundary value problem.First,the existence of the unique solution for linear boundary value problem is proved,and its Green＇s function is given.Finally,the existence of at least three positive solutions for the above problem is established by using Avery-Peterson fixed point theorem,when f satisfies some growth conditions.

关 键 词：三阶三点边值问题 不动点定理 正解 

分 类 号：O175.8[理学—数学]