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Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 421545, 9 pages
Research Article

Existence of a Period-Two Solution in Linearizable Difference Equations

Department of Mathematics, University of Rhode Island, Kingston, RI 02881-0816, USA

Received 28 August 2013; Accepted 8 October 2013

Academic Editor: Senada Kalabusic

Copyright © 2013 E. J. Janowski and M. R. S. Kulenović. 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.


Consider the difference equation where and the initial conditions are real numbers. We investigate the existence and nonexistence of the minimal period-two solution of this equation when it can be rewritten as the nonautonomous linear equation , where and the functions . We give some necessary and sufficient conditions for the equation to have a minimal period-two solution when .