Advances in Difference Equations
Volume 2007 (2007), Article ID 31272, 13 pages
Research Article

On a k-Order System of Lyness-Type Difference Equations

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

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

Received 17 January 2007; Revised 24 April 2007; Accepted 14 June 2007

Academic Editor: John R. Graef

Copyright © 2007 G. Papaschinopoulos 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.


We consider the following system of Lyness-type difference equations: x1(n+1)=(akxk(n)+bk)/xk1(n1), x2(n+1)=(a1x1(n)+b1)/xk(n1), xi(n+1)=(ai1xi1(n)+bi1)/xi2(n1), i=3,4,,k, where ai, bi, i=1,2,,k, are positive constants, k3 is an integer, and the initial values are positive real numbers. We study the existence of invariants, the boundedness, the persistence, and the periodicity of the positive solutions of this system.