# Portugaliae Mathematica

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**Volume 66, Issue 4, 2009, pp. 513–533**

**DOI: 10.4171/PM/1853**

An oscillation criterion for linear difference equations with general delay argument

G. E. Chatzarakis^{[1]}, Ch. G. Philos

^{[2]}and I. P. Stavroulakis

^{[3]}(1) Dept. of Mathematics, University of Ioannina, 45110, IOANNINA, GREECE

(2) Dept. of Mathematics, University of Ioannina, 45110, IOANNINA, GREECE

(3) Dept. of Mathematics, University of Ioannina, 45110, IOANNINA, GREECE

This paper presents a new sufficient condition for the oscillation of all solutions of linear difference equations with general delay argument. The significance of this condition is demonstrated by comparing with known oscillation conditions. An example illustrating the results is also given.

*Keywords: *Delay argument, difference equation, oscillatory solution, nonoscillatory solution

Chatzarakis G., Philos Ch., Stavroulakis I.: An oscillation criterion for linear difference equations with general delay argument. *Port. Math.* 66 (2009), 513-533. doi: 10.4171/PM/1853