New oscillation criteria for linear matrix Hamiltonian systems

Some new oscillation criteria are established for the matrix linear Hamiltonian system X′=A(t)X+B(t)Y, Y′=C(t)X−A∗(t)Y under the hypothesis: A(t), B(t)=B∗(t)>0, and C(t)=C∗(t) are n×n real continuous matrix functions on the interval t₀,∞), (−∞<t₀). These results are sharper than some previous results even for self-adjoint second order matrix differential systems.