**Author(s): ** Chunli Wang |

Xiaoshuang Han |

Xiaoshuang Li**Journal: ** Electronic Journal of Differential Equations ISSN 1072-6691

**Volume: ** 2008;

**Issue: ** 87;

**Start page: ** 1;

**Date: ** 2008;

Original page**Keywords: ** Boundary value problem |

positive solution |

difference equation |

fixed point |

changing sign coefficients**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 $n in [2, infty)$, $l in [1, n]$, $0 < a < 1$, $(1-a)l geq 2$, $(1+a)lleq n+1$, $f in C(mathbb{R}^+,mathbb{R}^+)$ 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.

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