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Oscillation criteria for linear matrix Hamiltonian systems


Author: G. A. Grigorian
Journal: Proc. Amer. Math. Soc. 148 (2020), 3407-3415
MSC (2010): Primary 34C10
DOI: https://doi.org/10.1090/proc/14973
Published electronically: March 17, 2020
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Abstract: The Riccati equation method is used to establish two new oscillation criteria for linear matrix Hamiltonian systems in a new direction, which is to break the positive definiteness restriction imposed on one of the coefficients of the Hamiltonian system. The obtained results are compared with some known oscillatory criteria.


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Additional Information

G. A. Grigorian
Affiliation: Institute of Mathematics of NAS of RA, 24/5 Marshal Bagramian Avenue, Yerevan, 0019, Republic of Armenia
Email: mathphys2@instmath.sci.am

DOI: https://doi.org/10.1090/proc/14973
Keywords: Riccati equation, Hamiltonian systems, conjoined solutions, oscillation, trace, nonnegative (positive) definiteness, the least eigenvalue of the hermitian matrix, separator
Received by editor(s): June 11, 2019
Received by editor(s) in revised form: November 26, 2019, December 9, 2019, and December 17, 2019
Published electronically: March 17, 2020
Communicated by: Wenxian Shen
Article copyright: © Copyright 2020 American Mathematical Society