Oscillation of partial difference equations with continuous variables

In this paper, we consider the partial difference equation with continuous variables of the form P1z(x + a, y + b) + p2z (x + a, y) + p3z (x, y + b) − p4z (x, y) + P (x, y) z (x − τ, y − σ) = 0, where P ϵ C(R+ × R+, R+ − {0}), a, b, τ, σ are real numbers and pi (i = 1, 2, 3, 4) are nonnegative constants. Some sufficient conditions for all solutions of this equation to be oscillatory are obtained.