Oscillation Criteria for Hamiltonian Matrix Difference 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.

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

Dilations‎, ‎models‎, ‎scattering and spectral problems of 1D discrete Hamiltonian systems

In this paper, the maximal dissipative extensions of a symmetric singular 1D discrete Hamiltonian operator with maximal deficiency indices (2,2) (in limit-circle cases at ±∞) and acting in the Hilbert space ℓ_{Ω}²(Z;C²) (Z:={0,±1,±2,...}) are considered. We consider two classes dissipative operators with separated boundary conditions both at -∞ and ∞. For each of these cases we establish a self...

Trigonometric Transformations of Sympletic Difference Systems

In this paper we show that any symplectic difference system can be transformed into a trigonometric system, using a transformation that preserves oscillatory properties. Necessary and sufficient conditions for nonoscillation of a certain class of trigonometric systems are given, and this result is applied to oscillation theory of Hamiltonian difference systems. 2000 Academic Press