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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 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
Full-text PDF (219 kB) Citations (2)
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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.
Received: 24.01.2008
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2010, Volume 54, Issue 4, Pages 62–71
DOI: https://doi.org/10.3103/S1066369X10040080
Bibliographic databases:
UDC: 517.968
Language: Russian
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
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\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://mathscinet.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{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-78649549597}
Linking options:
  • https://www.mathnet.ru/eng/ivm6727
  • https://www.mathnet.ru/eng/ivm/y2010/i4/p72
    • This publication is cited in the following 2 articles:
    1. 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
    2. 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
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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    Abstract page:475
    Full-text PDF :97
    References:50
    First page:3
     
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