Oscillation Criteria for Linear Matrix Hamiltonian Systems

Oscillation Criteria for Hamiltonian Matrix Difference Systems

We obtain some oscillation criteria for the Hamiltonian difference system (AY{t) = B{t)Y{t+\) + C{t)Z{t), I AZ{t) = -A{t)Y{t + 1) B*{t)Z{t), where A, B, C, Y, Z are dxd matrix functions. As a corollary, we establish the validity of an earlier conjecture for a second-order matrix difference system.

Oscillation Criteria Based on a New Weighted Function for Linear Matrix Hamiltonian Systems

Oscillation of Linear Hamiltonian Systems

We establish new oscillation criteria for linear Hamiltonian systems using monotone functionals on a suitable matrix space. In doing so we develop new criteria for oscillation involving general monotone functionals instead of the usual largest eigenvalue. Our results are new even in the particular case of self-adjoint second order differential systems.

Some Oscillation Results for Linear Hamiltonian Systems

The purpose of this paper is to develop a generalized matrix Riccati technique for the selfadjoint matrixHamiltonian systemU′ A t U B t V , V ′ C t U−A∗ t 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. ...

Interval oscillation criteria for matrix differential systems with damping

Using a generalized Riccati transformation, some new oscillation criteria of linear second order matrix differential system with damping are built by the method of integral average. These results are based on the information on a sequence of subintervals of [t0,∞). 2000 Mathematics Subject Classification: 34C10.