Positive Solutions of a Three-Point Boundary Value Problem
Received:October 30, 2005  Revised:July 20, 2006
Key Word: three-point boundary value problem   positive solution   cone   fixed point index.
Fund ProjectL:the Natural Science Foundation of Gansu Province (3ZS051-A25-016); NWNU-KJCXGC; the Spring-sun program (Z2004-1-62033).
 Author Name Affiliation HAN Xiao-ling Department of Mathematics, Northwest Normal University, Gansu 730070, China
Hits: 2432
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].