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On the stability of invariant sets of a system of autonomous differential equations under constantly acting perturbations

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Abstract

We consider a system of ordinary autonomous differential equations that has an invariant set. We obtain sufficient conditions for the stability of this system under constantly acting perturbations.

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References

  1. V. A. Pliss,Integral Sets of Periodic Systems of Differential Equations [in Russian], Nauka, Moscow (1977).

    MATH  Google Scholar 

  2. A. M. Samoilenko,Elements of the Mathematical Theory of Multifrequency Oscillations [in Russian], Nauka, Moscow (1987).

    Google Scholar 

  3. Yu. A. Mitropol'skii and O. B. Lykova,Integral Manifolds in Nonlinear Mechanics [in Russian], Moscow (1973).

  4. N. Rouche, P. Habets, and M. Laloy,Stability Theory by Liapunov's Direct Method, Springer, New York (1977).

    MATH  Google Scholar 

  5. A. Ya. Savchenko and A. O. Ignat'ev,Some Problems of Stability of Nonautonomous Dynamic Systems [in Russian], Naukova Dumka, Kiev (1989).

    Google Scholar 

  6. V. I. Zubov,Stability of Motion [in Russian], Vysshaya Shkola, Moscow (1973).

    Google Scholar 

  7. A. O. Ignat'ev, “Application of the Lyapunov direct method to the investigation of integral sets,”Ukr. Mat. Zh.,44, No. 10, 1342–1348 (1992).

    MATH  MathSciNet  Google Scholar 

  8. N. N. Krasovskii,Some Problems in the Theory of Stability of Motion [in Russian], Fizmatgiz, Moscow (1959).

    Google Scholar 

  9. V. E. Germaidze and N. N. Krasovskii, “On stability under constantly acting perturbations,”Prikl. Mat. Mekh.,21, No. 6, 769–774 (1957).

    MathSciNet  Google Scholar 

  10. E. A. Barbashin and N. N. Krasovskii, “On global stability of motion,”Dokl. Akad. Nauk SSSR,86, No. 3, 453–456 (1952).

    MATH  Google Scholar 

  11. A. O. Ignat'ev, “On the existence of Lyapunov functions in the problems of stability of integral sets,”Ukr. Mat. Zh.,45, No. 7, 932–941 (1993).

    Article  MathSciNet  Google Scholar 

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Authors
  1. A. O. Ignat'ev
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  2. B. I. Konosevich
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Additional information

Institute of Applied Mathematics and Mechanics, Ukrainian Academy of Sciences, Donetsk. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 9, pp. 1287–1291, September, 1999.

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Ignat'ev, A.O., Konosevich, B.I. On the stability of invariant sets of a system of autonomous differential equations under constantly acting perturbations. Ukr Math J 51, 1448–1453 (1999). https://doi.org/10.1007/BF02593011

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  • DOI: https://doi.org/10.1007/BF02593011

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