Geodesic
On the Aizerman Problem for Systems of Two Differential Equations
Matematičeskie zametki, Tome 105 (2019) no. 2, pp. 240-250 Cet article a éte moissonné depuis la source Math-Net.Ru

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The stability of equilibria of systems of nonlinear ordinary differential equations is studied. A criterion for the reducibility of a second-order linear system to a scalar differential equation is given. Both positive definite and semidefinite Lyapunov functions are used to obtain sufficient conditions for the asymptotic stability (global stability) of second-order nonlinear differential equations. It is proved that the Aizerman problem has a positive solution with respect to the roots of the characteristic equation of two-dimensional systems of differential equations.
Keywords: system of differential equations, equilibrium, stability, Aizerman problem, Lyapunov functions. 
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     author = {B. S. Kalitin},
     title = {On the {Aizerman} {Problem} for {Systems} of {Two} {Differential} {Equations}},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2019_105_2_a5/}
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B. S. Kalitin. On the Aizerman Problem for Systems of Two Differential Equations. Matematičeskie zametki, Tome 105 (2019) no. 2, pp. 240-250. http://geodesic.mathdoc.fr/item/MZM_2019_105_2_a5/

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