New oscillation criteria for linear matrix Hamiltonian systems (Q5917522)

The author establishes some new oscillation criteria for the linear matrix Hamiltonian system \[ X'=A(t)X+B(t)Y, \qquad Y'=C(t)X-A^*(t)Y, \] under the hypothesis: \(A(t), B(t)=B^*(t)>0\) and \(C(t)=C^*(t)\) are real continuous \(n\times n\)-matrix functions on the interval \([t_0,\infty)\), where the matrix \(M^*\) denote the conjugate transpose of the matrix \(M\). These results are sharper than some previous results even for selfadjoint second-order matrix differential systems.