This article is cited in 2 papers

On the Aizerman Problem for Systems of Two Differential Equations

B. S. Kalitin

Belarusian State University

Abstract: 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.

UDC: 517.925

Received: 24.01.2018

DOI: 10.4213/mzm11939

 English version: Mathematical Notes, 2019, 105:2, 227–235

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