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On the influence of integral perturbations to the asymptotic stability of solutions of a second-order linear differential equation

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Abstract

Sufficient conditions for the asymptotic stability of the solutions of a second-order linear integro-differential equation of the Volterra type are established in the case where the solutions of the corresponding second-order linear differential equation may have no property under study. Thus, the influence of integral perturbations on the asymptotic stability of solutions of linear differential equations of the second order is revealed. For this purpose, the method of auxiliary kernels is developed. An illustrative example is given.

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Authors and Affiliations

  1. Institute of Mathematics of the NAS of the Kyrgyz Republic, Bishkek-71, Kyrgyzstan

    Samandar Iskandarov

  2. Osh State University, Osh, Kyrgyzstan

    Nazigai A. Abdiraiimova

Authors
  1. Samandar Iskandarov
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  2. Nazigai A. Abdiraiimova
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Correspondence to Samandar Iskandarov.

Additional information

Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 17, No. 2, pp. 188–195 April–June, 2020.

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Iskandarov, S., Abdiraiimova, N.A. On the influence of integral perturbations to the asymptotic stability of solutions of a second-order linear differential equation. J Math Sci 249, 733–738 (2020). https://doi.org/10.1007/s10958-020-04969-w

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  • DOI: https://doi.org/10.1007/s10958-020-04969-w

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