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Transactions of the American Mathematical Society

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Total stability of sets for nonautonomous differential systems

Author: Zhivko S. Athanassov
Journal: Trans. Amer. Math. Soc. 295 (1986), 649-663
MSC: Primary 34D10; Secondary 34D20, 93D05
MathSciNet review: 833701
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Abstract: The principal purpose of this paper is to present sufficient conditions for total stability, or stability under constantly acting perturbations, of sets of a sufficiently general kind for nonautonomous ordinary differential equations. To do this, two Liapunov-like functions with specific properties are used. The obtained results include and considerably improve the classical results on total stability of isolated equilibrium points. Applications are presented to study the stability of nonautonomous Lurie-type nonlinear equations.

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Keywords: Total stability of sets, nonautonomous differential systems, Liapunovlike functions, Lurie-type equations, uniform asymptotic stability, absolute stability
Article copyright: © Copyright 1986 American Mathematical Society