Electronic Journal of Differential Equations,
Vol. 2008(2008), No. 87, pp. 1-10.

Title: Positive solutions to nonlinear second-order three-point boundary-value
       problems for difference equation with change of sign
  
Authors: Chunli Wang (Univ. of Electronic Technology, Guilin, Guangxi, China)
         Xiaoshuang Han (Yanbian Univ. Yanji, Jilin, China)
	 Chunhong Li    (Yanbian Univ. Yanji, Jilin, China)
 
Abstract: 
 In this paper we investigate the existence of positive solution to
 the  discrete second-order three-point boundary-value problem
 $$\displaylines{
 \Delta^2 x_{k-1}+ h(k) f(x_k)=0, \quad  k \in [1, n], \cr
 x_0 =0,  \quad  a x_l = x_{n+1},
 }$$
 where  $n \in [2, \infty)$, $l \in [1, n]$, $0 < a < 1$,
 $(1-a)l \geq 2$, $(1+a)l\leq n+1$, $f \in C(\mathbb{R}^+,\mathbb{R}^+)$ 
 and $h(t)$ is a function that may change sign on $[1, n]$.
 Using the fixed-point index theory, we prove the existence of
 positive solution for the above boundary-value problem.
 
Submitted March 6, 2008. Published June 11, 2008.
Math Subject Classifications: 39A05, 39A10.
Key Words: Boundary value problem; positive solution;
           difference equation; fixed point; changing sign coefficients.