Riccati techniques and oscillation for self-adjoint matrix Hamiltonian systemsI

The purpose of this paper is to develop a generalized matrix Riccati technique for the self- adjoint matrix Hamiltonian system U0 D A.x/U C B.x/V; V0 D 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.