Discrete Dynamics in Nature and Society
Volume 2011 (2011), Article ID 308362, 11 pages
http://dx.doi.org/10.1155/2011/308362
Research Article

Solvability of a Class of Generalized Neumann Boundary Value Problems for Second-Order Nonlinear Difference Equations

Jianye Xia1 and Yuji Liu2

1Department of Applied Mathematics, Guangdong University of Finance, Guangzhou 510000, China
2Department of Mathematics, Guangdong University of Business Studies, Guangzhou 510000, China

Received 18 April 2011; Accepted 17 June 2011

Academic Editor: Hassan A. El-Morshedy

Copyright © 2011 Jianye Xia and Yuji Liu. 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

This paper is motivated by Rachnkovab and Tisdell (2006) and Anderson et al. (2007). New sufficient conditions for the existence of at least one solution of the generalized Neumann boundary value problems for second order nonlinear difference equations ∇ Δ 𝑥 ( 𝑘 ) = 𝑓 ( 𝑘 , 𝑥 ( 𝑘 ) , 𝑥 ( 𝑘 + 1 ) ) , 𝑘 ∈ [ 1 , 𝑛 − 1 ] , 𝑥 ( 0 ) = 𝑎 𝑥 ( 1 ) , 𝑥 ( 𝑛 ) = 𝑏 𝑥 ( 𝑛 − 1 ) , are established.