一类三点边值问题正解的存在性

在与线性问题第一特征值相关的条件下,通过应用不动点指数理论讨论了三点边值问题u″ 9(t)f(u)=0,t∈(0,1),u′(0)=0,u(1)=αu(η)正解的存在性,这里η∈(0,1),α∈R且0<α<1.本文结果推广和改进了文献1]的主要结论.

Positive Solutions of a Three-Point Boundary Value Problem

We study the existence of positive solutions of the three-point boundary value problem $u'+g(t)f(u)=0,\ \ t\in(0,\ 1),$ $ u'(0)=0,\qquad u(1)=\alpha u(\eta), $ where $\eta\in(0,1)$, and $\alpha \in \mathbb{R}$ with We study the existence of positive solutions of the three-point boundary value problem $u'+g(t)f(u)=0,\ \ t\in(0,\ 1),$ $ u'(0)=0,\qquad u(1)=\alpha u(\eta), $ where $\eta\in(0,1)$, and $\alpha \in \mathbb{R}$ with We study the existence of positive solutions of the three-point boundary value problem $$u'+g(t)f(u)=0,\ \ t\in(0,\ 1),$$ $$ u'(0)=0,\qquad u(1)=\alpha u(\eta), $$ where $\eta\in(0,1)$, and $\alpha \in \mathbb{R}$ with $0<\alpha<1$. The existence of positive solutions is studied by means of fixed point index theory under some conditions concerning the first eigenvalue with respect to the relevant linear operator. The results here essentially extend and improve the main result in 1].