Abstract :
In this paper, we consider the following forced higher-order nonlinear neutral difference equation
Δm(xn + cnxn−k )+
u
s=1
p
(s)
n fs (xn−rs ) = qn, n n0,
where m,u 1, k 0, and rs 0 are integers, {cn}, {p
(s)
n } (s = 1, 2, . . . ,u) and {qn} are sequence of
real numbers and fs ∈ C(R,R) (s = 1, 2, . . . , u). By using Krasnoselskii’s fixed point theorem and
some new techniques, we obtain sufficient conditions for the existence of nonoscillatory solutions
for general {p
(s)
n } (s = 1, 2, . . . ,u) and {qn} which means that we allow oscillatory {p
(s)
n } (s = 1, 2, . . . ,u) and {qn}.
2003 Elsevier Science (USA). All rights reserved.
