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

Yuan, Huting; Zhang, Guang; Zhao, Hongliang

doi:https://doi.org/10.1155/2007/49293

Discrete Dynamics in Nature and Society

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Research Article | Open Access

Volume 2007 | Article ID 049293 | https://doi.org/10.1155/2007/49293

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

Huting Yuan,¹Guang Zhang,²and Hongliang Zhao³

Received26 Jul 2006

Revised21 Nov 2006

Accepted22 Nov 2006

Published25 Dec 2006

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.

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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.

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