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 argumentsΔτN[X(t)−PX(t−γ)]+∑j=1nQj(t)X(t−σj)=0, where ΔτX(t)=X(t+τ)−X(t)ΔτX(t)=X(t+τ)−X(t), N⩾1N⩾1, P∈Rm×mP∈Rm×m, Qj∈C(R+,Rm×m)Qj∈C(R+,Rm×m), j=1,2,…,nj=1,2,…,n; τ, γ   and σjσj, j=1,2,…,nj=1,2,…,n, are non-negative constants. Furthermore, assume Qj(t)=((qj)lk(t))Qj(t)=((qj)lk(t)), where ((qj)lk(t))((qj)lk(t)), l,k=1,2,…,ml,k=1,2,…,m, j=1,2,…,nj=1,2,…,n, are continuous, bounded and do not change signs on R+R+.