Oscillations of two-dimensional nonlinear partial difference systems

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 Ni = {i, i + 1,…}, i is a nonnegative integer, T(Δ1, Δ2) = Δ1 + Δ2 + I, Δ1ymn = ym+1,n − ymn, Δ2ymn = ym,n+1 − ymn, Imnymn = Ymn, {amn} and {bmn} are real sequences, m, n ε N0, and f, g : R → R are continuous with of uf(u) > 0 and ug(u) > 0 for all u ≠ 0. A solution ({xmn}, {ymn}) of this system is oscillatory if both components are oscillatory. Some sufficient conditions are derived for all solutions of this system to be oscillatory.