非线性三点边值问题正解的存在性

本文研究了三点边值问题{u″-k2u+a(t)f(u)=0,t∈(0,1),u(0)=0,u(1)=αu(η)正解的存在性,其中a∈C(0,1],0,∞)),η∈(0,1),α∈(0,sinh(k)/sinh(kη)),f∈C(0,∞),0,∞)).主要结果的证明基于锥上的不动点定理.

Existence of positive solutions for nonlinear three-point boundary value problem

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.