Oscillation criteria of Yan type for linear Hamiltonian systems (Q597332)

Consider the linear Hamiltonian system \[ X'=A(t)X+B(t)Y,\quad Y'=C(t)X-A^*(t)Y , \] where \(X(t)\), \(Y(t)\), \(A(t)\), \(B(t)\) and \(C(t)\) are \(n\times n\)-matrix functions, \(B\) and \(C\) are symmetric and \(B\) is positive definite. The authors derive new oscillation criteria for this system. The main tool is the Riccati-type transformation and an application of the method of weighted integral averages and the nonnegative weighting function \(H(t,s)\), originally due to \textit{Ch. G. Philos} [Arch. Math. 53, 482--492 (1989; Zbl 0661.34030)] (for ordinary differential equations).