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New oscillation criteria for linear matrix Hamiltonian systems. (English) Zbl 1032.34032
The author establishes some new oscillation criteria for the linear matrix Hamiltonian system $$X'=A(t)X+B(t)Y, \qquad Y'=C(t)X-A^*(t)Y,$$ under the hypothesis: $A(t), B(t)=B^*(t)>0$ and $C(t)=C^*(t)$ are real continuous $n\times n$-matrix functions on the interval $[t_0,\infty)$, where the matrix $M^*$ denote the conjugate transpose of the matrix $M$. These results are sharper than some previous results even for selfadjoint second-order matrix differential systems.

##### MSC:
 34C10 Qualitative theory of oscillations of ODE: zeros, disconjugacy and comparison theory 34A30 Linear ODE and systems, general
##### Keywords:
oscillation; linear; Hamiltonian system
Full Text:
##### References:
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