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Journal of Mathematical Sciences

, Volume 230, Issue 5, pp 683–687 | Cite as

On a Method of Study of Specific Asymptotic Stability of Solutions to a Sixth-Order Linear Integrodifferential Volterra Equation

  • S. Iskandarov
Article
  • 7 Downloads

Abstract

We state sufficient conditions of the asymptotic stability on the semi-axis of solutions to a linear, homogeneous, sixth-order integrodifferential Volterra-type equation in the case where solutions of the corresponding linear, homogeneous, sixth-order differential equation are asymptotically unstable. We also present a new method and an illustrating example.

Keywords and phrases

integrodifferential equation specific asymptotic stability method of squaring method of shearing functions Lyusternik–Sobolev lemma 

AMS Subject Classification

53A40 20M15 

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Notes

References

  1. 1.
    Yu. A. Ved’ and Z. Pakhyrov, “Sufficient conditions of the boundedness of solutions to linear integrodifferential equations,” in: Research in Integrodifferintial Equations in Kyrgyzstan [in Russian], 9, Ilim, Frunze (1973), pp. 68–103.Google Scholar
  2. 2.
    M. I. Imanaliev and S. Iskandarov, “Specific condition of stability of solutions to a fourth-order linear homogeneous Volterra integrodifferential equation,” Dokl. Ross. Akad. Nauk, 425, No. 4, 447–451 (2009).zbMATHGoogle Scholar
  3. 3.
    S. Iskandarov, Method of Weight and Shearing Functions and Asymptotic Properties of Solutions to Integrodifferential and Integral Equations of Volterra Type [in Russian], Ilim, Bishkek (2002).Google Scholar
  4. 4.
    S. Iskandarov, “On a nonstandard method of the study of asymptotic stability of solutions to a fourth-order linear integrodifferential Volterra equation,” in: Research in Integrodifferintial Equations in Kyrgyzstan [in Russian], 44, Ilim, Frunze (2012), pp. 44–51.Google Scholar
  5. 5.
    S. Iskandarov, “Method of study of asymptotic stability of solutions to a fifth-order linear integrodifferential Volterra equation,” in: Research in Integrodifferintial Equations in Kyrgyzstan [in Russian], 46, Ilim, Frunze (2014), pp. 41-48.Google Scholar
  6. 6.
    L. A. Lyusternik and V. I. Sobolev, Elements of Functional Analysis, Frederick Ungar, New York; Constable, London (1961).Google Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of Theoretical and Applied Mathematics of the National Academy of Sciences of the Kyrgyz RepublicBishkekKyrgyzstan

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