Electronic Journal of Differential Equations,
Vol. 2008(2008), No. 41, pp. 1-7.

Title: Existence of positive solution for semipositone 
       second-order three-point boundary-value problem
 
Authors: Jian-Ping Sun (Lanzhou Univ. Technology,Gansu, China)
         Jia Wei       (Lanzhou Univ. Technology,Gansu, China)

Abstract: 
 In this paper, we establish the existence of positive solution for
 the semipositone second-order three-point boundary value problem
 $u''(t)+\lambda f(t,u(t))=0$, $0<t<1$,
 $u(0)=\alpha u(\eta)$, $ u(1)=\beta u(\eta)$.
 Our arguments are based on the well-known Guo-Krasnosel'skii
 fixed-point theorem in cones.
 
Submitted August 28, 2007. Published March 20, 2008.
Math Subject Classifications: 34B15.
Key Words: Semipositone; boundary value problem; positive solution; 
           existence; fixed-point.