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∈N 0={0,1,2,…}, T(Δ 1,Δ 2)=Δ 1+Δ 2+I, T(∇1,∇2)=∇1+∇2+I, Δ 1 y mn =y m+1,n −y mn , Δ 2 y mn =y m,n+1−y mn , Iy mn =y mn , ∇1 y mn =y m−1,n −y mn , ∇2 y mn =y m,n−1−y mn , {a mn } and {b mn } are real sequences, m,n∈N 0, and f,g:R→R are continuous with uf(u)>0 and ug(u)>0 for all u≠0. A solution ({x mn },{y mn }) of the system is oscillatory if both components are oscillatory. Some sufficient conditions for all solutions of this system to be oscillatory are derived.