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Matematicheskie Zametki, 2018, Volume 103, Issue 6, Pages 831–840
DOI: https://doi.org/10.4213/mzm10637 (Mi mzm10637) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Stability Criterion for Systems of Two First-Order Linear Ordinary Differential Equations

G. A. Grigoryan

Institute of Mathematics, National Academy of Sciences of Armenia, Yerevan
Full-text PDF (469 kB) Citations (2)
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DOI: https://doi.org/10.4213/mzm10637
Abstract: The method of Riccati's equation is applied to find a stability criterion for systems of two first-order linear ordinary differential equations. The obtained result is compared for a particular example with results obtained by the Lyapunov and Bogdanov methods, by using estimates of solutions of systems in terms of the Losinskii logarithmic norms, and by the freezing method.
Keywords: Riccati's equation, normal and limit solutions, Lyapunov stability, instability, logarithmic norms.
Received: 20.12.2017
English version:
Mathematical Notes, 2018, Volume 103, Issue 6, Pages 892–900
DOI: https://doi.org/10.1134/S0001434618050255
Bibliographic databases:
Document Type: Article
UDC: 517.923
Language: Russian
Citation: G. A. Grigoryan, “Stability Criterion for Systems of Two First-Order Linear Ordinary Differential Equations”, Mat. Zametki, 103:6 (2018), 831–840; Math. Notes, 103:6 (2018), 892–900
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
    1. S. G. Bulanov, “Kriterii ustoichivosti po Lyapunovu sistem obyknovennykh differentsialnykh uravnenii v multiplikativnoi i additivnoi forme”, Materialy 5 Mezhdunarodnoi konferentsii «Dinamicheskie sistemy i kompyuternye nauki: teoriya i prilozheniya» (DYSC 2023). Irkutsk, 18-23 sentyabrya 2023 g., Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 234, VINITI RAN, M., 2024, 108–117  mathnet  crossref
    2. Gevorg A. Grigorian, “Stability criteria for systems of two first-order linear ordinary differential equations”, Mathematica Slovaca, 72:4 (2022), 935  crossref  mathscinet
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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