Oscillation for partial difference equations with continuous variables

In this paper, we develop criteria for oscillation of the partial difference equation with continuous variables of the form Au(x+a,y+b) + Bu(x+a,y) + Cu(x,y+b) - u(x,y) + D(x,y)u(x-τ,y) + E(x,y)u(x,y-σ) + F(x,y)u(x-τ,y-σ) = 0, where D,E,F ∈ C(R+ × R+, R+ - {0}), A,B and C are nonnegative constants, a, b, τ and σ are positive constants. Several examples which dwell upon the importance of our results are also included.