Oscillation for linear non-autonomous systems of difference equations with continuous arguments

In this paper, we establish sufficient conditions for the oscillation of the linear non-autonomous systems of difference equations with continuous arguments Nτ X(t)−PX(t −γ ) + n j=1 Qj (t)X(t −σj ) = 0, where τ X(t) = X(t +τ)−X(t), N 1, P ∈ Rm×m, Qj ∈ C(R+,Rm×m), j = 1, 2, . . . , n; τ , γ and σj , j = 1, 2, . . . , n, are non-negative constants. Furthermore, assume Qj (t) = ((qj )lk(t)), where ((qj )lk(t)), l, k = 1, 2, . . . , m, j = 1, 2, . . . , n, are continuous, bounded and do not change signs on R+. © 2006 Elsevier Inc. All rights reserved.