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Method of limiting equations for the stability analysis of equations with infinite delay in the Carathéodory conditions: I

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Abstract

We consider systems of nonautonomous nonlinear differential equations with infinite delay. We introduce Carathéodory type conditions for the right-hand side in an equation, which permit one, on the one hand, to cover a fairly broad class of systems and, on the other hand, include the right-hand side in a compact function space and construct the so-called limiting equations. In the investigation, we use the construction of admissible spaces with fading memory, which permits one to obtain constructive results for the class of equations under study.

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Authors and Affiliations

  1. Computer Center, Russian Academy of Sciences, Moscow, Russia

    O. V. Druzhinina & N. O. Sedova

  2. Ul’yanovsk State University, Ul’yanovsk, Russia

    O. V. Druzhinina & N. O. Sedova

Authors
  1. O. V. Druzhinina
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  2. N. O. Sedova
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Correspondence to O. V. Druzhinina.

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Original Russian Text © O.V. Druzhinina, N.O. Sedova, 2014, published in Differentsial’nye Uravneniya, 2014, Vol. 50, No. 5, pp. 572–583.

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Druzhinina, O.V., Sedova, N.O. Method of limiting equations for the stability analysis of equations with infinite delay in the Carathéodory conditions: I. Diff Equat 50, 569–580 (2014). https://doi.org/10.1134/S0012266114050012

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