Oscillation and nonoscillation for difference equations with variable delays

In this paper, we obtain some sharp conditions for oscillation and nonoscillation of the difference equation with variable delays (GRAPHICS) where m is a positive integer, {k(i)(n)}(n=n0)(infinity) and {p(i)(n)}(n=n0)(infinity) (i=1,2,...,m) are sequences of positive integers and real numbers, respectively. Our results improve and extend/complement known results in the literature. (C) 2003 Elsevier Ltd. All rights reserved.