Advances in Difference Equations 
Volume 2008 (2008), Article ID 932831, 22 pages
doi:10.1155/2008/932831
Research Article

Asymptotic Representation of the Solutions of Linear Volterra Difference Equations

István Győri and László Horváth

 Department of Mathematics and Computing, University of Pannonia, 8200 Veszprém, Egyetem u. 10, Hungary
Received 26 February 2008; Accepted 4 April 2008

Recommended by Elena Braverman

Abstract

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.