Oscillatory behavior of delay partial difference equations with positive and negative coefficients

We construct an important transform to obtain sufficient conditions for the oscillation of all solutions of delay partial difference equations with positive and negative coefficients of the form Am+1,n + Am,n+1 − Amn + pmnAm−k−1 − qmnAm−k′,n−l′ = 0, where m, n = 0, 1, …, and k, k′, l′, l are nonnegative integers, p, q ε (0, ∞), the coefficients {qmn} and {pmn} are sequences of nonnegative real numbers.