%0 Journal Article
%T 非线性三点边值问题正解的存在性<br>Existence of positive solutions for nonlinear three-point boundary value problem
%A 李涛涛
%J 四川大学学报 (自然科学版)
%D 2017
%X 本文研究了三点边值问题 \[ \begin{cases} u''-k^{2}u+a(t)f(u)=0,~~t\in(0,1),\u(0)=0,~~u(1)=\alpha u(\eta) \end{cases} \] 正解的存在性,~其中~$a\in C([0,1],[0,\infty)),~\eta\in(0,1),~\alpha\in\Big(0,\frac{\sinh(k)}{\sinh(k\eta)}\Big),~f\in C([0,\infty),[0,\infty))$.~主要结果的证明基于锥上的不动点定理.<br>In this paper,~we study the existence of positive solutions for second-order three-point boundary value problem \[ \begin{cases} u''-k^{2}u+a(t)f(u)=0,~~t\in(0,1),\u(0)=0,~~u(1)=\alpha u(\eta), \end{cases} \] where~$a\in C([0,1],[0,\infty)),~\eta\in(0,1),~\alpha\in\Big(0,\frac{\sinh(k)}{\sinh(k\eta)}\Big),~f\in C([0,\infty),[0,\infty))$.~The proof of the main result is based on fixed point theorem
%K Green~函数 ~边值问题 ~不动点定理 ~正解&lt
%K br&gt
%K Green's function ~Boundary value problem ~Fixed point theorem ~Positive solution
%U http://science.ijournals.cn/jsunature_cn/ch/reader/view_abstract.aspx?file_no=Z160537&flag=1