First, an oscillation theorem is presented for the n-th order delay differential equation \[ (r(t)x'(t))(n-1)+∑k_{i=1}fi(t)Fi(xτ_i(t), x'τ_i(t), ..., x(n-1)τ_i(t))=b(t), \ \ r(t)>0.\] Then the asymptotic behavior of bounded oscillatory solutions of the above equations is investigated.
In his paper [3], K. Oshima characterized a certain classes of submultiplicative matrix norms. It is intent of this paper to extend his work. The main result will be given in the diagram.