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The fixed sign property of solutions and stability of linear differential equations with varying distributed delay

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Abstract

We study one class of linear differential equations with varying distributed delay. We obtain an effective (in terms of parameters of the initial problem) criterion for the positivity of the Cauchy function of this class of equations. Based on this result, we establish effective criteria for the exponential stability of equations under consideration.

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Authors and Affiliations

  1. Perm State Technical University, Komsomol’skii pr. 29a, Perm, 614000, Russia

    V. V. Malygina & T. L. Sabatulina

Authors
  1. V. V. Malygina
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  2. T. L. Sabatulina
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Correspondence to V. V. Malygina.

Additional information

Original Russian Text © V.V. Malygina and T.L. Sabatulina, 2008, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2008, No. 8, pp. 73–77.

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Malygina, V.V., Sabatulina, T.L. The fixed sign property of solutions and stability of linear differential equations with varying distributed delay. Russ Math. 52, 61–64 (2008). https://doi.org/10.3103/S1066369X08080082

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  • DOI: https://doi.org/10.3103/S1066369X08080082

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