Oscillation theorems for self-adjoint matrix Hamiltonian systems

By using generalized Riccati technique, linear positive functional and the weighted averages technique, some new oscillation criteria for self-adjoint Hamiltonian matrix system are obtained. These results generalize and improve earlier results due to Kumari and Umamaheswaram [9] for (E), Parhi and Praharaj [12], Etgen and Pawlowski [6] for (P(x)U′(x))′+Q(x)U(x)=0 or its special cases, and Coles [3] for the scalar system y″(x)+q(x)y(x)=0.