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