This paper studies the following nonlinear two-dimensional partial difference system:
Δ1(xmn−bmng(ymn)=0,
T(Δ1Δ2)(ymn+amnf(xmn)=0,
where m, n
ϵ
N
i
= {i, i + 1,…}, i is a nonnegative integer, T(Δ
1, Δ
2) = Δ
1 + Δ
2 + I, Δ
1
y
mn
= y
m+1,n
− y
mn
, Δ
2
y
mn
= y
m,n+1 − y
mn
, I
mn
y
mn
= Y
mn
, {a
mn
} and {b
mn
} are real sequences, m, n
ϵ
N
0, and f, g : R → R are continuous with of uf(u) > 0 and ug(u) > 0 for all u ≠ 0. A solution ({x
mn
}, {y
mn
}) of this system is oscillatory if both components are oscillatory. Some sufficient conditions are derived for all solutions of this system to be oscillatory.
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