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)V U ? = 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.
oscillation matrix hamiltonian system matrix riccati technique integral averaging technique monotone functionals