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+σXm(t)Q(t)X*m(t)]Xσ(t)=0. These results extend and unify earlier results for the differential and difference equation case.