On the Aizerman Problem for Systems of Two Differential Equations
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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.
Keywordssystem of differential equations equilibrium stability Aizerman problem Lyapunov functions
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