Linear transformation and oscillation criteria for 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 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. ...

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

Stability criteria for linear Hamiltonian dynamic systems on time scales

* Correspondence: tangxh@mail. csu.edu.cn School of Mathematical Sciences and Computing Technology, Central South University, Changsha 410083, Hunan, P.R. China Full list of author information is available at the end of the article Abstract In this article, we establish some stability criteria for the polar linear Hamiltonian dynamic system on time scales x (t) = α(t)x(σ (t)) + β(t)y(t), y (t) ...