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Exponent Estimation for Stable Solutions of a Certain Class of Differential-Difference Equations

Abstract

For a differential-difference equation with a positive fundamental solution we obtain exponential stability conditions with exact estimates of the exponent and the coefficient of the exponential decay. These estimates are expressed in terms of the largest of two possible real roots of the characteristic function. We prove that one can obtain exact estimates for any solution by estimating the fundamental solution, taking into account the norm of the initial function. We establish two-sided estimates for the fundamental solution in the case, when equation parameters are given as intervals.

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Funding

This work was supported by the Ministry of Education and Science of the Russian Federation, state assignment FSNM-2020-0028.

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Correspondence to V. V. Malygina.

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Russian Text © The Author(s), 2021, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2021, No. 12, pp. 67–79.

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Malygina, V.V. Exponent Estimation for Stable Solutions of a Certain Class of Differential-Difference Equations. Russ Math. 65, 56–67 (2021). https://doi.org/10.3103/S1066369X21120069

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  • DOI: https://doi.org/10.3103/S1066369X21120069

Keywords

  • functional differential equation
  • fundamental solution
  • exponential stability
  • exponent estimate