Advances in Difference Equations
Volume 2010 (2010), Article ID 789302, 20 pages
doi:10.1155/2010/789302
Research Article

Asymptotic Constancy in Linear Difference Equations: Limit Formulae and Sharp Conditions

István Győri and László Horváth

Department of Mathematics, University of Pannonia, Egyetem u. 10. Veszprém 8200, Hungary

Received 20 January 2010; Accepted 23 March 2010

Academic Editor: Ağacik Zafer

Copyright © 2010 István Győri and László Horváth. 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

It is found that every solution of a system of linear delay difference equations has finite limit at infinity, if some conditions are satisfied. These are much weaker than the known sufficient conditions for asymptotic constancy of the solutions. When we impose some positivity assumptions on the coefficient matrices, our conditions are also necessary. The novelty of our results is illustrated by examples.