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Mat. Zametki, 2018, Volume 103, Issue 6, Pages 831–840 (Mi mz10637)  

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

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.

DOI: https://doi.org/10.4213/mzm10637

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English version:
Mathematical Notes, 2018, 103:6, 892–900

Bibliographic databases:

UDC: 517.923
Received: 20.12.2017

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

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