Advances in Difference Equations
Volume 2004 (2004), Issue 1, Pages 1-10
An asymptotic result for some delay difference equations with continuous variable
Department of Mathematics, University of Ioannina, P.O. Box 1186, Ioannina 45110, Greece
Received 14 October 2003
Copyright © 2004 Ch. G. Philos and I. K. Purnaras. 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.
We consider a nonhomogeneous linear delay difference equation with continuous variable and establish an asymptotic result for the solutions. Our result is obtained by the use of a positive root with an appropriate property of the so called characteristic equation of the corresponding homogeneous linear (autonomous) delay difference equation. More precisely, we show that, for any solution, the limit of a specific integral transformation of it, which depends on a suitable positive root of the characteristic equation, exists as a real number and it is given explicitly in terms of the positive root of the characteristic equation and the initial function.