Interval criteria for oscillationof linear 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) ...

Stability criteria for linear Hamiltonian systems under impulsive perturbations

where p(t) and q(t) are real-valued functions and p(t) 6= 0 for any t ∈ R. In what follows we assume that a(t), b(t), and c(t) satisfy the periodicity conditions a(t+ T ) = a(t), b(t+ T ) = b(t), c(t+ T ) = c(t), t ∈ R. The system (2) (or (3)) is said to be stable if all solutions are bounded on R, unstable if all nontrivial solutions are unbounded on R, and conditionally stable if there exits ...

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.

Linear Hamiltonian systems

We study linear Hamiltonian systems using bilinear and quadratic differential forms. Such a representation-free approach allows to use the same concepts and techniques to deal with systems isolated from their environment and with systems subject to external influences, and allows to study systems described by higher-order differential equations, thus dispensing with the usual point of view in c...

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