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Asymptotic behavior of the resolvent of an unstable volterra equation with kernel depending on the difference of the arguments

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Abstract

We present the structure of the resolvent of a difference kernel, which allows us to study the asymptotic behavior of the solution of the renewal equation for a given asymptotic behavior of the constant term. An asymptotic representation for the resolvent is obtained under minimal requirements on the moments of the kernel. Similar results are given for integro-differential equations.

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Authors and Affiliations

  1. Kuban State University, Krasnodar

    V. A. Derbenev & Z. B. Tsalyuk

Authors
  1. V. A. Derbenev
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  2. Z. B. Tsalyuk
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Translated fromMatematicheskie Zametki, Vol. 62, No. 1, pp. 88–94, July, 1997.

Translated by M. A. Shishkova

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Derbenev, V.A., Tsalyuk, Z.B. Asymptotic behavior of the resolvent of an unstable volterra equation with kernel depending on the difference of the arguments. Math Notes 62, 74–79 (1997). https://doi.org/10.1007/BF02356066

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  • DOI: https://doi.org/10.1007/BF02356066

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