Riccati techniques and oscillation for self-adjoint matrix Hamiltonian systems

The purpose of this paper is to develop a generalized matrix Riccati technique for the self-adjoint matrix Hamiltonian system U′=A(x)U+B(x)V,V′=C(x)U−A∗(x)VU′=A(x)U+B(x)V,V′=C(x)U−A∗(x)V. Together with the integral averaging technique and monotone functionals, new oscillation and interval oscillation criteria are established for the system. These criteria extend, improve, complement a number of existing results, and handle some cases not covered by known criteria. In particular, two interesting examples are included to illustrate the versatility of our results.