Oscillation theorems for self-adjoint matrix Hamiltonian systems

AbstractBy using generalized Riccati technique, linear positive functional and the weighted averages technique, some new oscillation criteria for self-adjoint Hamiltonian matrix system (E)U′(x)=A(x)U(x)+B(x)V(x),V′(x)=C(x)U(x)−A∗(x)V(x)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