Discrete Dynamics in Nature and Society
Volume 2010 (2010), Article ID 419536, 15 pages
doi:10.1155/2010/419536
Research Article

Positive Periodic Solutions of Nonlinear First-Order Functional Difference Equations

Ruyun Ma, Tianlan Chen, and Yanqiong Lu

Department of Mathematics, Northwest Normal University, Lanzhou 730070, China

Received 12 October 2010; Accepted 19 December 2010

Academic Editor: Marko Robnik

Copyright © 2010 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

We consider the existence, multiplicity, and nonexistence of positive 𝑇 -periodic solutions for the difference equations Δ 𝑥 ( 𝑛 ) = 𝑎 ( 𝑛 ) 𝑔 ( 𝑥 ( 𝑛 ) ) 𝑥 ( 𝑛 ) − 𝜆 𝑏 ( 𝑛 ) 𝑓 ( 𝑥 ( 𝑛 − 𝜏 ( 𝑛 ) ) ) , and Δ 𝑥 ( 𝑛 ) + 𝑎 ( 𝑛 ) 𝑔 ( 𝑥 ( 𝑛 ) ) 𝑥 ( 𝑛 ) = 𝜆 𝑏 ( 𝑛 ) 𝑓 ( 𝑥 ( 𝑛 − 𝜏 ( 𝑛 ) ) ) , where 𝑎 , 𝑏 ∶ ℤ → [ 0 , ∞ ) are 𝑇 -periodic, 𝜏 ∶ ℤ → ℤ is 𝑇 -periodic.