Oscillation of self-adjoint linear matrix Hamiltonian systems

By means of monotone functionals defined on suitable matrix spaces and new methods, oscillation criteria for self-adjoint linear Hamiltonian matrix system of the form X (x) = A(x)X(x) + B(x)Y(x), Y (x) = C(x)X(x) − A∗(x)Y (x), are obtained. There results are sharper than some previous results even for self-adjoint second-order matrix differential systems. In particular, our theorems are generalizations and improvements of many existing results including those obtained by Sun [J. Math. Anal. Appl. 279 (2003) 651–658].  2004 Elsevier Inc. All rights reserved.