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Izv. Vyssh. Uchebn. Zaved. Mat., 2010, Number 4, Pages 72–82 (Mi ivm6727)  

This article is cited in 2 scientific papers (total in 2 papers)

The resolvent structure of a Volterra equation with nonsummable difference kernel

Z. B. Tsalyuk, M. V. Tsalyuk

Chair of Differential and Integral Equations, Kuban State University, Krasnodar, Russia

Abstract: In this paper we study the asymptotic behavior of the resolvent of a linear integral Volterra equation whose difference kernel is nonsummable. For a certain class of such kernels the equation is reducible to an equation whose difference kernel is summable. This enables one to use the well-known results on the structure of resolvents of summable kernels in the case of a nonsummable kernel. We apply the obtained results to homogeneous kernels of degree $-1$.

Keywords: linear integral Volterra equation, nonsummable kernel, resolvent structure, homogeneous kernel.

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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2010, 54:4, 62–71

Bibliographic databases:

UDC: 517.968
Received: 24.01.2008

Citation: Z. B. Tsalyuk, M. V. Tsalyuk, “The resolvent structure of a Volterra equation with nonsummable difference kernel”, Izv. Vyssh. Uchebn. Zaved. Mat., 2010, no. 4, 72–82; Russian Math. (Iz. VUZ), 54:4 (2010), 62–71

Citation in format AMSBIB
\Bibitem{TsaTsa10}
\by Z.~B.~Tsalyuk, M.~V.~Tsalyuk
\paper The resolvent structure of a~Volterra equation with nonsummable difference kernel
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2010
\issue 4
\pages 72--82
\mathnet{http://mi.mathnet.ru/ivm6727}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2779414}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2010
\vol 54
\issue 4
\pages 62--71
\crossref{https://doi.org/10.3103/S1066369X10040080}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-78649549597}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Z. B. Tsalyuk, M. V. Tsalyuk, “The asymptotic behavior of solutions of a certain nonlinear Volterra equation”, Russian Math. (Iz. VUZ), 56:7 (2012), 30–38  mathnet  crossref  mathscinet
    2. I. L. Oinas, T. A. Sivacheva, Z. B. Tsalyuk, “The structure of the resolvent for the discrete renewal equation with nonsummable difference kernel”, Russian Math. (Iz. VUZ), 58:5 (2014), 21–29  mathnet  crossref
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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