Open Access

An asymptotic result for some delay difference equations with continuous variable

Advances in Difference Equations20042004:679264

https://doi.org/10.1155/S1687183904310058

Received: 14 October 2003

Published: 24 March 2004

Abstract

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.

Authors’ Affiliations

(1)
Department of Mathematics, University of Ioannina

Copyright

© Philos and Purnaras 2004