Discrete Dynamics in Nature and Society

Discrete Dynamics in Nature and Society / 2007 / Article

Research Article | Open Access

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

Huting Yuan, Guang Zhang, Hongliang Zhao, "Existence of Positive Solutions for a Discrete Three-Point Boundary Value Problem", Discrete Dynamics in Nature and Society, vol. 2007, Article ID 049293, 14 pages, 2007. https://doi.org/10.1155/2007/49293

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

Received26 Jul 2006
Revised21 Nov 2006
Accepted22 Nov 2006
Published25 Dec 2006

Abstract

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.

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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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