Discrete Dynamics in Nature and Society
Volume 2007 (2007), Article ID 49293, 14 pages
doi:10.1155/2007/49293

Existence of positive solutions for a discrete three-point boundary value problem

Huting Yuan1 , Guang Zhang2 and Hongliang Zhao3

1Department of Mathematics, Yanbei Normal University, Datong, Shanxi 037000, China
 2School of Science, Tianjin University of Commerce, Tianjin 300134, China
 3Department of Mathematics, Qingdao Technological University, 11 Fushun Road, Qingdao 266033, China

Abstract

A discrete three-point boundary value problem Δ2xk−1+λfk(xk)=0, k=1,2,…,n, x0=0, axl=xn+1, is considered, where 1≤l≤n is a fixed integer, a is a real constant number, and λ is a positive parameter. A characterization of the values of λ is carried out so that the boundary value problem has the positive solutions. Particularly, in this paper the constant a can be negative numbers. The similar results are not valid for the three-point boundary value problem of differential equations.