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Open Access Open Badges Research Article

An asymptotic result for some delay difference equations with continuous variable

Ch G Philos* and IK Purnaras

Author Affiliations

Department of Mathematics, University of Ioannina, P.O. Box 1186, Ioannina 45110, Greece

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Advances in Difference Equations 2004, 2004:679264  doi:10.1155/S1687183904310058

The electronic version of this article is the complete one and can be found online at: http://www.advancesindifferenceequations.com/content/2004/1/679264

Received:14 October 2003
Published:24 March 2004

© 2004 Philos and Purnaras

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.

Research Article