Oscillation for nonlinear 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 the delay partial difference equations with positive and negative coefficients of the form ωƒ(m, n, Am−σ,n−τ, Am−u,n−v) + Am−1,n + Am,n−1 − Amn + pAm+k,n+l − qAm+k′,n+l′ = 0, and ωmnƒ(m, n, Am−σ,n−τ, Am−u,n−v) + Am−1,n + Am,n−1) − Amn + pmnAm+k,n+l − qmnAm+k′,n+l′ = 0, where m, n = 0,1, …, and k, k′, l′, l are nonnegative integers, ω,p,q (0,∞), and σ, τ, u, v are positive integers. The coefficients {ωmn}, {qmn}, and {pmn} are assumed to be positive.