New oscillation criteria for linear matrix Hamiltonian systems

Abstract

Some new oscillation criteria are established for the matrix linear Hamiltonian system X′= A( t) X+ B( t) Y, Y′=C(t)X−A ∗(t)Y under the hypothesis: A( t), B(t)=B ∗(t)>0 , and C(t)=C ∗(t) are n× n real continuous matrix functions on the interval [ t 0,∞), (−∞< t 0). These results are sharper than some previous results even for self-adjoint second order matrix differential systems.