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On the stability problem for functional differential equations with infinite delay

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Abstract

We study the stability of functional differential equations with infinite delay, using the Lyapunov functional of constant sign with a derivative of constant sign. Limit equations are constructed in a special phase space. We establish a theorem on localization of a positive limit set and theorems on the stability and the asymptotic stability. The results are illustrated by examples.

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References

  1. J. K. Hale and J. Kato, “Phase Space for Retarded Equations with Infinite Delay,” Funk. Ekv. 21, 11–41 (1978).

    MATH  MathSciNet  Google Scholar 

  2. J. Haddock and J. Terjeki, “On the Location of Positive Limit Sets for Autonomous Functional Differential Equations with Infinite Delay,” J. Different. Equat. 86, 1–32 (1990).

    Article  MATH  MathSciNet  Google Scholar 

  3. J. Kato and T. Yoshizawa, “Remarks on Global Properties in Limiting Equations,” Funk. Ekv. 24, 363–371 (1981).

    MATH  MathSciNet  Google Scholar 

  4. N. O. Sedova, “On the Lyapunov—Razumikhin Method for Equations with Infinite Delay,” Differents. Uravneniya 38(10), 1338–1347 (2002).

    MathSciNet  Google Scholar 

  5. A. S. Andreev and S. V. Pavlikov, “Non-Sign-Definite Lyapunov Functionals in the Stability Problem for Functional Differential Equations with Finite Delay,” Mekhan. Tverd. Tela 34, 112–118 (2004).

    MathSciNet  Google Scholar 

  6. A. S. Andreev and D. Kh. Khusanov, “On the Method of Lyapunov Functionals in the Problem on Stability and Instability,” Differents. Uravneniya 34(7), 876–885 (1998).

    MATH  MathSciNet  Google Scholar 

  7. S. V. Pavlikov, “Sign-Constant Lyapunov Functionals in the Stability Problem for Functional Differential Equations with Finite Delay,” in Uchen. Zap. Ulyanovsk. Gos. Univ. “Fundamental Problems of Mathematics and Mechanics” (Ulyanovsk. Gos. Univ., 2002), No. 2, pp. 30–39.

  8. J. Kato, “Stability Problem in Functional Differential Equations with Infinite Delay,” Funk. Ekv. 21, 63–80 (1978).

    MATH  Google Scholar 

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Authors and Affiliations

  1. Kama State Engineering-Economics Academy, pr. Mira 68/19, Naberezhnye Chelny, 423810, Russia

    S. V. Pavlikov

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  1. S. V. Pavlikov
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Correspondence to S. V. Pavlikov.

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Original Russian Text © S.V. Pavlikov, 2008, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2008, No. 7, pp. 29–38.

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Pavlikov, S.V. On the stability problem for functional differential equations with infinite delay. Russ Math. 52, 24–32 (2008). https://doi.org/10.3103/S1066369X08070049

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  • DOI: https://doi.org/10.3103/S1066369X08070049

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