Some Oscillation Results for Linear Hamiltonian Systems

Abstract

The purpose of this paper is to develop a generalized matrix Riccati technique for the selfadjoint matrix Hamiltonian system $U^{\prime }=A\left(t\right)U+B\left(t\right)V$, $V^{\prime }=C\left(t\right)U-A^{\ast }\left(t\right)V$. By using the standard integral averaging technique and positive functionals, new oscillation and interval oscillation criteria are established for the system. These criteria extend and improve some results that have been required before. An interesting example is included to illustrate the importance of our results.