%0 Journal Article
%T On Positive Solutions of Second-order Three-point Boundary Value Problem<br>二阶三点边值问题的正解
%A Wang shuli
%A Liu Jinsheng
%A <br>王淑丽
%A 刘进生
%J 数学物理学报(A辑)
%D 2008
%I 
%X In this paper, the existence of positive solutions of the second-order three-point boundary value problem $-u'(t)=b(t)f(u(t))$ for all $t\in0,1]$ subject to $u'(0)=0$, $u(1)={\alpha}u({\eta})$ is studied, where $\alpha, \eta\in(0,1)$ are given, $f\in C\big(0,\infty),0,\infty)\big)$, $b\in C\big(0,1],0,\infty)\big)$ and there exists $t_0\in0,1]$ such that $b(t_0)>0$. The problem is transformed into the Hammerstein's integral equation with its corresponding Green's funtion. By applying the fixed point index theory, authors obtain the optimal sufficient conditions for the existence of single and multiple positive solutions of the above mentioned problem concerning the first eigenvalue of the relevant linear problem.
%K Positive solutionszz
%K Conezz
%K Fixed point indexzz
%K First eigenvaluezz<br>正解
%K 锥
%K 不动点指数
%K 第一特征值.
%K 二阶三点边值问题
%K 正解存在
%K Boundary
%K Value
%K Problem
%K 充分性条件
%K 最佳
%K 第一特征值
%K 线性问题
%K 指数理论
%K 不动点
%K 积分方程
%K Hammerstein
%K 转化
%K 函数
%K Green
%K 利用
%K 常数
%K 多重性
%K 存在性
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=6E709DC38FA1D09A4B578DD0906875B5B44D4D294832BB8E&cid=37F46C35E03B4B86&jid=4DB553CDB5F521D8C921082E5C95EC80&aid=6BFE59C322977FB964EADBED019A1F37&yid=67289AFF6305E306&vid=D3E34374A0D77D7F&iid=0B39A22176CE99FB&sid=F4BDB5452F9F5642&eid=9C82B18080268586&journal_id=1003-3998&journal_name=数学物理学报(A辑)&referenced_num=0&reference_num=13