%0 Journal Article
%T 非线性微分方程三阶三点边值问题正解的存在性<br>Existence of positive solutions for a third-order three-point boundary value problem of nonlinear differential equations
%A 郭丽君
%J 山东大学学报（理学版）
%D 2016
%R 10.6040/j.issn.1671-9352.0.2016.243
%X 摘要： 三阶微分方程有着广泛的应用背景和重要的理论价值,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),其中0<br>Abstract: The third order differential equation has a wide application background and an important theoretical value, Green function plays an important role in the existence of positive solutions for the third order three point boundary value problems. This paper is concerned with the following boundary value problem{u(t)+a(t)f(u(t))=0, t∈(0,1),u(0)=u″(0)=0, u'(1)=αu(η),where 0 1 and 0 1 /η. By establishing Green function for the associated linear boundary value problem, the solution for the above boundary value problem is obtained. Then some existence criteria of at least two positive solutions are obtained by using the fixed point index theorem
%K 正解
%K 三阶三点边值问题
%K 存在性
%K 格林函数
%K 不动点指数理论
%K 锥
%K &lt
%K br&gt
%K fixed point index theorem
%K existence
%K Green function
%K third-order three-point boundary value problem
%K cone
%K positive solution
%U http://lxbwk.njournal.sdu.edu.cn/CN/10.6040/j.issn.1671-9352.0.2016.243