Discrete Dynamics in Nature and Society
Volume 2007 (2007), Article ID 49293, 14 pages
Research Article

Existence of Positive Solutions for a Discrete Three-Point Boundary Value Problem

Huting Yuan,1 Guang Zhang,2 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

Received 26 July 2006; Revised 21 November 2006; Accepted 22 November 2006

Copyright © 2007 Huting Yuan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A discrete three-point boundary value problem Δ2xk1+λfk(xk)=0, k=1,2,,n, x0=0, axl=xn+1, is considered, where 1ln 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.