Necessary and sufficient conditions for the oscillation of systems of difference equations with continuous arguments ✩

In this paper the oscillation of all solutions of system of the form y(t)+ n i=1 Piy(t −τi ) = 0, where Pi ∈ Rm×m, τi ∈ R (i = 1, 2, . . . , n), is studied. Necessary and sufficient conditions in terms of the characteristic equation and explicit conditions in terms of the eigenvalues or the logarithmic norms of the coefficient matrices are established.  2005 Elsevier Inc. All rights reserved