Oscillation Criteria for Hamiltonian Matrix Difference 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

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.

Oscillation criteria for two-dimensional difference systems of first order linear difference equations

Sufficient conditions are established for the oscillation of the linear two-dimensional difference system ∆xn = pn yn, ∆yn−1 = −qnxn, n ∈ N (n0) = {n0, n0 + 1, . . .}, where {pn}, {qn} are nonnegative real sequences. Our results extend the results in the literature. c © 2007 Elsevier Ltd. All rights reserved.

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. ...