Advances in Difference Equations
Volume 2009 (2009), Article ID 327649, 11 pages
doi:10.1155/2009/327649
Research Article

On the Recursive Sequence xn+1=A+(xn−1p/xnq)

C. J. Schinas, G. Papaschinopoulos, and G. Stefanidou

School of Engineering, Democritus University of Thrace, 67100 Xanthi, Greece

Received 11 June 2009; Revised 10 September 2009; Accepted 21 September 2009

Academic Editor: Ağacik Zafer

Copyright © 2009 C. J. Schinas 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

In this paper we study the boundedness, the persistence, the attractivity and the stability of the positive solutions of the nonlinear difference equation xn+1=α+(xn−1p/xnq), n=0,1,…, where α,p,q∈(0,∞) and x−1,x0∈(0,∞). Moreover we investigate the existence of a prime two periodic solution of the above equation and we find solutions which converge to this periodic solution.