Discrete Dynamics in Nature and Society
Volume 2007 (2007), Article ID 40963, 9 pages
Research Article

On the Recursive Sequence xn+1=A+xnp/xn1r

Stevo Stević

Mathematical Institute of the Serbian Academy of Science, Knez Mihailova 35/I, Beograd 11000, Serbia

Received 1 October 2007; Accepted 5 November 2007

Copyright © 2007 Stevo Stević. 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.


The paper considers the boundedness character of positive solutions of the difference equation xn+1=A+xnp/xn1r, n0, where A, p, and r are positive real numbers. It is shown that (a) If p24r>4, or p1+r, r1, then this equation has positive unbounded solutions; (b) if p2<4r, or 2rp<1+r, r(0,1), then all positive solutions of the equation are bounded. Also, an analogous result is proved regarding positive solutions of the max type difference equation xn+1=max{A,xnp/xn1r}, where A, p, q(0,).