Oscillations of nonlinear partial difference systems

This paper studies the following two-dimensional nonlinear partial difference systems [GRAPHICS] where m, n is an element of N-0 = {0, 1, 2,...), T(Delta(1), Delta(2)) = Delta(1) + Delta(2) + I, T(del(1) , del(2)) = del(1) + del(2) + I, Delta(1) y(mn) = y(m) + 1,n -y(mn), Delta(2)y(mn) = y(m,n) + 1 - Y-mn, Iy(mn) = y(mn), del(1) y(mn) = y(m-1,n) - y(mn), del(2) y(mn) = y(m,n-1)- 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 the system is oscillatory if both components are oscillatory. Some sufficient conditions for all solutions of this system to be oscillatory are derived. (C) 2002 Elsevier Science (USA). All rights reserved.