Sufficient conditions for the oscillation of linear difference equations with variable delay

Linear difference equations with variable delay are considered. The most important result of this paper is a new oscillation criterion, which should be looked upon as the discrete analogue of a well-known oscillation criterion for first order linear delay differential equations. This criterion constitutes a substantial improvement of an oscillation result due to the first author (Funkcial. Ekvac. 34 (1991), pp. 157-172). The results obtained extend the ones by the authors and Stavroulakis (J. Differ. Equ. Appl. 10 (2004), pp. 419-435) concerning the special case of linear difference equations with constant delay.