摘要
格林函数在三阶三点边值问题的正解存在性理论中有着重要作用.考虑以下三阶三点边值问题{u'''(t)+a(t)f(u(t))=0,t∈(0,1),u(0)=u″(0)=0,u'(1)-αu(η)=λ,其中,0<η<1,0<α<1/η,参数λ∈(0,∞).通过建立相关线性边值问题的格林函数得到解的形式,运用Guo-Krasnoselskii不动点定理建立上述边值问题至少一个正解的存在性准则.
The Green function plays an important role in the existence of positive solutions for the third-order three-point boundary value problems.In this paper,we consider the following boundary value problem{um（t）＋a（t）f（u（t））=0,t∈（0,1）∪u（0）=un（0）=0,u＇（1）-αu（η）=λ.}where 0〈η 〈1,0〈α 〈1/η,and λ∈（0,∞） is a parameter.By establishing Green function for the related linear boundary value problem,the existence result of the positive solution for the problem considered is established by using Guo-Krasnoselskii fixed point theorem.
作者
郭丽君
GUO Lijun(Department of Electronic and Information Engineering, Lanzhou Jiaotong University Bowen College, Lanzhou 730101, Gansu)
出处
《四川师范大学学报（自然科学版）》
CAS
北大核心
2016年第6期846-850,共5页
Journal of Sichuan Normal University（Natural Science）
基金
甘肃省高等学校科研项目(2015B-214)
关键词
三阶三点边值问题
正解
存在性
锥
格林函数
不动点定理
third-order three-point boundary value problem
positive solution
existence
cone
Green function
fixed point theorem
