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On the existence of Lyapunov functions in problems of stability of integral sets

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Ukrainian Mathematical Journal Aims and scope

Abstract

A nonautonomous system of ordinary differential equations is considered. If this system admits a uniformly asymptotically stable integral set, then a neighborhood of this set contains a function similar to the Lyapunov function.

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Authors and Affiliations

  1. Institute of Applied Mathematics and Mechanics, Ukrainian Academy of Sciences, Donetsk

    A. O. Ignat'ev

Authors
  1. A. O. Ignat'ev
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Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 7, pp. 932–941, July, 1993.

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Ignat'ev, A.O. On the existence of Lyapunov functions in problems of stability of integral sets. Ukr Math J 45, 1031–1041 (1993). https://doi.org/10.1007/BF01057450

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  • DOI: https://doi.org/10.1007/BF01057450

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