Equivalence of the Oscillation of Two Coupled Difference Systems

In this paper, we establish the equivalence of the oscillation of the following two coupled differential systems Delta[xi(n)-timesi(n-T_i)] +P_i(n)f_i x₁ (n-T_i), ... , times_m (n-T_im)) = 0 and Delta²y_i (n-i) + P_i(n)-T_i f_i (y_i(n), ... , y_m (n)) = 0 where p_i (n) : Z⁺rarr R⁺,T_i isin Z for i, j = 1, ... , m, f_i (u₁, ... , u_m) is nondecreasing in u_i for i = 1, ... , m and satisfies the following conditions { f_i (u₁, ... , u_m )> 0 if u_i > 0 for i = 1, ... ,m, f_i (u₁, ... , u_m ) < 0 if u_i < 0 for i = 1, ... , m.