The Riccati equation method is used to establish some new oscillatory criteria for Hamiltonian systems in a new direction, which is to break the positive definiteness restriction imposed on one of coefficients of the Hamiltonian system. The obtained results are compared with some well known ones.
"Interval oscillation criteria for linear matrix Hamiltonian systems." Rocky Mountain J. Math. 50 (6) 2047 - 2057, December 2020. https://doi.org/10.1216/rmj.2020.50.2047