Atkinson’s super-linear oscillation theorem for matrix dynamic equations on a time scale

By applying the Riccati technique and operator theory, we establish on a time scale T both oscillation and non-oscillation criteria for Atkinson’s super-linear matrix dynamic equation XΔ2 + [Xm(t)Q(t)X∗m(t )]σXσ (t ) = 0. These results extend and unify earlier results for the differential and difference equation case.  2004 Elsevier Inc. All rights reserved