Geodesic
On the Aizerman Problem for Systems of Two Differential Equations
Matematičeskie zametki, Tome 105 (2019) no. 2, pp. 240-250

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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. 
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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