Oscillations of two-dimensional nonlinear partial difference systems

This paper studies the following nonlinear two-dimensional partial difference system: Delta(1)(x(mn)) - b(mng)(y(mn)) = 0, T(Delta(1), Delta(2)) (y(mn)) + a(mn)f(x(mn)) = 0, where m, n is an element of N-i = {i, i + 1,...}, i is a nonnegative integer, T(Delta(1), Delta(2)) = Delta(1) + Delta(2) + I, Delta(1ymn) = y(m+1,n) - y(mn), Delta(2ymn) = y(mn,n+1) - y(mn), I(mn)y(mn) = y(mn), {a(mn)} and {b(mn)} are real sequences, m, n is an element of N-0, and f, g : R --> R are continuous with uf(u) > 0 and ug(u) > 0 for all u not equal 0. A solution ({x(mn)), {y(mn)) of this system is oscillatory if both components are oscillatory. Some sufficient conditions are derived for all solutions of this system to be oscillatory. (C) 2004 Elsevier Ltd. All rights reserved.