非线性三阶三点边值问题正解的存在性  

Existence of positive solution for a nonlinear third-order three-point boundary value problem

作　　者：孙建平[1] 张小丽[1] 

机构地区：[1]兰州理工大学理学院,甘肃兰州730050

出　　处：《西北师范大学学报（自然科学版）》2012年第3期1-4,31,共5页Journal of Northwest Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(10801068)

摘　　要：讨论非线性三阶三点边值问题u''(t)+a(t)f(u(t))=0,t∈[0,1],u(0)=u′(0)=0,u(1)=αu′(η).在给出相应的Green函数并讨论其性质的基础上,运用Guo-Krasnoselskii不动点定理获得了上述三阶三点边值问题正解的存在性.This paper is concerned with the following nonlinear third-order three-point boundary value problem {u＇＇（t）＋a（t）f（u（t））=0,t∈,u（0）=u′（0）=0,u（1）=αu′（η）.The corresponding Green＇s function is given and its properties are discussed.And then,the existence of positive solution for the above boundary value problem is obtained by using the Guo-Krasnoselskii fixed point theorem.

关 键 词：三阶三点边值问题 GREEN函数 正解 存在性 不动点 

分 类 号：O175.8[理学—数学]