Geodesic
Stability Criterion for Systems of Two First-Order Linear Ordinary Differential Equations
Matematičeskie zametki, Tome 103 (2018) no. 6, pp. 831-840

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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.
Mots-clés : Riccati's equation, normal and limit solutions
Keywords: Lyapunov stability, instability, logarithmic norms. 
@article{MZM_2018_103_6_a2,
     author = {G. A. Grigoryan},
     title = {Stability {Criterion} for {Systems} of {Two} {First-Order} {Linear} {Ordinary} {Differential} {Equations}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {831--840},
     publisher = {mathdoc},
     volume = {103},
     number = {6},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2018_103_6_a2/}
}
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G. A. Grigoryan. Stability Criterion for Systems of Two First-Order Linear Ordinary Differential Equations. Matematičeskie zametki, Tome 103 (2018) no. 6, pp. 831-840. http://geodesic.mathdoc.fr/item/MZM_2018_103_6_a2/