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Application of the direct method of Lyapunov to the analysis of integral sets

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Abstract

The concepts are defined of the stability, attraction, and asymptotic stability of the integral sets of systems of ordinary differential equations. With the use of the second method of Lyapunov, a number of theorems are proved concerning the stability of integral sets.

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Authors and Affiliations

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

    A. O. Ignat'ev

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  1. A. O. Ignat'ev
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Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 10, pp. 1342–1348, October, 1992.

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Ignat'ev, A.O. Application of the direct method of Lyapunov to the analysis of integral sets. Ukr Math J 44, 1229–1235 (1992). https://doi.org/10.1007/BF01057679

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  • DOI: https://doi.org/10.1007/BF01057679

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