Oscillation criteria for matrix Hamiltonian systems via the summability method (Q734592)

By using the summability method and Riccati transformation, the author studies the oscillation of the following linear matrix Hamiltonian system \[ \begin{cases} X'=A(t)X+B(t)U,\\ U'=C(t)X-A^{*}(t)U, \;t\geq0. \end{cases} \] Some new oscillation criteria are established, which improve and generalize some known results of \textit{G. J. Butler, H. L. Erbe} and \textit{A. B. Mingarelli} [Trans. Am. Math. Soc. 303, 263--282 (1987; Zbl 0648.34031)], \textit{W. J. Coles} and \textit{M. K. Kinyon} [Rocky Mt. J. Math. 24, 19--36 (1994; Zbl 0807.34042)] and \textit{P. Hartman} [Proc. Am. Math. Soc. 64, 251--259 (1977; Zbl 0412.34017)].