Discrete Dynamics in Nature and Society
Volume 2011 (2011), Article ID 624157, 12 pages
http://dx.doi.org/10.1155/2011/624157
Research Article

Global Structure of Positive Solutions of a Discrete Problem with Sign-Changing Weight

Ruyun Ma,1 Chenghua Gao,1 Xiaoling Han,1 and Xiaoqiang Chen2

1Department of Mathematics, Northwest Normal University, Lanzhou 730070, China
2School of Automation and Electrical Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China

Received 27 April 2011; Accepted 28 June 2011

Academic Editor: Zengji Du

Copyright © 2011 Ruyun Ma 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.

Abstract

Let 𝑇 > 5 be an integer, 𝕋 = { 1 , 2 , … , 𝑇 } . We are concerned with the global structure of positive solutions set of the discrete second-order boundary value problems Δ 2 𝑢 ( 𝑡 − 1 ) + 𝑟 𝑚 ( 𝑡 ) 𝑓 ( 𝑢 ( 𝑡 ) ) = 0 , 𝑡 ∈ 𝕋 , 𝑢 ( 0 ) = 𝑢 ( 𝑇 + 1 ) = 0 , where 𝑟 ∈ ℝ is a parameter, 𝑚 ∶ 𝕋 → ℝ changes its sign and 𝑚 ( 𝑡 ) ≠ 0 f o r 𝑡 ∈ 𝕋 .