Abstract
In this paper, we obtain some sharp conditions for oscillation and nonoscillation of the difference equation with variable delays
χ
n+1−χ
n+
∑
i=1
m
Pi(n)χ
n-ki(n)=0, n⩽n0
where
m is a positive integer, {
k
i
(
n)}
n=
n
0
∞ and {
p
i
(
n)}
n=
n
0
∞, (
i = 1, 2,…,
m) are sequences of positive integers and real numbers, respectively. Our results improve and extend/complement known results in the literature.