Abstract
In this paper, we consider the following higher-order neutral difference equation: Δ
m
(
x
n
+
cx
n−k
) +
p
nx
n−r
= 0,
n ≥
n
0, where
c ϵ
R
,
m ≥ 1 is an odd integer,
k ≥ 1,
r ≥ 0 are integers, {
p
n
}
n=n
0
∞ is a sequence of real numbers. We obtain the global result (with respect to
c) for general {
p
n
}, which means that we allow oscillatory {itp
n}. The main result is a sufficient condition for the existence of nonoscillatory solutions.