Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 151, pp. 1-7.

Title: Multiple positive solutions for second-order three-point
       boundary-value problems with sign changing nonlinearities

Authors: Jian  Liu  (Shandong Univ. of Finance and Economics, China)
         Zengqin Zhao (Qufu Normal Univ., Qufu, Shandong, China)

Abstract:
 In this article, we study the second-order three-point boundary-value
 problem
 $$\displaylines{
 u''(t)+a(t)u'(t)+f(t,u)=0,\quad  0 \leq t \leq 1,   \cr
 u'(0)=0,\quad u(1)=\alpha u(\eta),
 }$$
 where $0<\alpha$, $\eta<1$, $a\in C([0,1],(-\infty, 0))$ and $f$ is
 allowed to change sign. We show that there exist two positive
 solutions by using Leggett-Williams fixed-point theorem.

Submitted March 14, 2012. Published September 07, 2012.
Math Subject Classifications: 34B15, 34B25.
Key Words: Multiple positive solutions; sign changing; fixed-point theorem.