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)+∑i=1nPiy(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.