Abstract
Consider the higher order nonlinear partial difference equation of neutral type
(∗)
Δ
n
h
Δ
m
r
(
y
(
m
,
n
)
+
c
y
(
m
−
k
,
n
−
l
)
)
+
F
(
m
,
n
,
y
(
m
−
τ
,
n
−
σ
)
)
=
0
,
where
h
,
r
∈
N
(
1
)
,
k
,
l
,
τ
,
σ
∈
N
(
0
)
,
c
∈
R
and
F
:
N
×
N
×
R
→
R
. In this paper, we first establish the discrete Arzela–Ascoli's theorem. Next, we obtain some sufficient conditions for the existence of bounded and unbounded nonoscillatory solution of Eq.
(∗).