Oscillations of nonlinear partial difference systems ✩

This paper studies the following two-dimensional nonlinear partial difference systems T (∇1,∇2)(xmn) + bmng(ymn) = 0, T (Δ1,Δ2)(ymn)+ amnf (xmn) = 0, where m,n ∈ N0 = {0, 1, 2, . . .}, T (Δ1,Δ2) = Δ1 +Δ2 + I , T (∇1,∇2)=∇1 +∇2 + I , Δ1ymn = ym+1,n−ymn,Δ2ymn = ym,n+1−ymn, Iymn = ymn, ∇1ymn = ym−1,n−ymn, ∇2ymn = ym,n−1− ymn, {amn} and {bmn} are real sequences, m,n ∈ N0, and f, g :R → R are continuous with uf (u) > 0 and ug(u) > 0 for all u = 0. A solution ({xmn}, {ymn}) of the system is oscillatory if both components are oscillatory. Some sufficient conditions for all solutions of this system to be oscillatory are derived.  2002 Elsevier Science (USA). All rights reserved.