Advances in Difference Equations
Volume 2008 (2008), Article ID 932831, 22 pages
Asymptotic Representation of the Solutions of Linear Volterra Difference Equations
Department of Mathematics and Computing, University of Pannonia, 8200 Veszprém, Egyetem u. 10, Hungary
Received 26 February 2008; Accepted 4 April 2008
Academic Editor: Elena Braverman
Copyright © 2008 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.
This article analyses the asymptotic behaviour of solutions of linear Volterra difference
equations. Some sufficient conditions are presented under which the solutions to a general
linear equation converge to limits, which are given by a limit formula. This result is then
used to obtain the exact asymptotic representation of the solutions of a class of convolution
scalar difference equations, which have real characteristic roots. We give examples showing
the accuracy of our results.