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On the Aizerman Problem for Systems of Two Differential Equations

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Abstract

The stability of equilibria of systems of nonlinear ordinary differential equations is studied. Acriterion for the reducibility of a second-order linear systemto 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.

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Authors and Affiliations

  1. Belarusian State University, Minsk, 220030, Belarus

    B. S. Kalitine

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  1. B. S. Kalitine
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Correspondence to B. S. Kalitine.

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Russian Text © B. S. Kalitine, k]2019, k]published in Matematicheskie Zametki, k]2019, k]Vol. 105, k]No. 2, k]pp. 240–250.

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Kalitine, B.S. On the Aizerman Problem for Systems of Two Differential Equations. Math Notes 105, 227–235 (2019). https://doi.org/10.1134/S0001434619010255

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  • DOI: https://doi.org/10.1134/S0001434619010255

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