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Matematicheskie Zametki, 1997, Volume 62, Issue 1, Pages 88–94
DOI: https://doi.org/10.4213/mzm1590 (Mi mzm1590) 		 
This article is cited in 10 scientific papers (total in 10 papers)

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

V. A. Derbenev, Z. B. Tsalyuk

Kuban State University
Full-text PDF (168 kB) Citations (10)
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DOI: https://doi.org/10.4213/mzm1590
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.
Received: 17.07.1995
English version:
Mathematical Notes, 1997, Volume 62, Issue 1, Pages 74–79
DOI: https://doi.org/10.1007/BF02356066
Bibliographic databases:
UDC: 517.9
Language: Russian
Citation: V. A. Derbenev, Z. B. Tsalyuk, “Asymptotic behavior of the resolvent of an unstable Volterra equation with kernel depending on the difference of the arguments”, Mat. Zametki, 62:1 (1997), 88–94; Math. Notes, 62:1 (1997), 74–79
Citation in format AMSBIB
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\issue 1
\pages 88--94
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\transl
\jour Math. Notes
\yr 1997
\vol 62
\issue 1
\pages 74--79
\crossref{https://doi.org/10.1007/BF02356066}
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Linking options:
  • https://www.mathnet.ru/eng/mzm1590
  • https://doi.org/10.4213/mzm1590
  • https://www.mathnet.ru/eng/mzm/v62/i1/p88
    • This publication is cited in the following 10 articles:
    1. Wang T., Qin M., Lian H., “The Asymptotic Approximations to Linear Weakly Singular Volterra Integral Equations Via Laplace Transform”, Numer. Algorithms, 85:2 (2020), 683–711  crossref  isi
    2. Z. B. Tsalyuk, M. V. Tsalyuk, “The resolvent structure of a Volterra equation with nonsummable difference kernel”, Russian Math. (Iz. VUZ), 54:4 (2010), 62–71  mathnet  crossref  mathscinet
    3. M. S. Sgibnev, “An asymptotic expansion of the solution to a system of integrodifferential equations with exact asymptotics for the remainder”, Siberian Math. J., 49:3 (2008), 524–538  mathnet  crossref  mathscinet  zmath  isi
    4. Sgibnev, MS, “Asymptotic expansion of the solution of an integro-differential equation with exact asymptotics of the remainder”, Differential Equations, 44:4 (2008), 551  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    5. Sgibnev, MS, “Asymptotics of solutions of an integro-differential and an integral equation”, Differential Equations, 42:9 (2006), 1291  mathnet  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    6. T. O. Kolbineva, Z. B. Tsalyuk, “Asymptotic behavior of solutions of a class of integral equations”, Russian Math. (Iz. VUZ), 48:2 (2004), 33–39  mathnet  mathscinet  zmath
    7. Tsalyuk, ZB, “Asymptotics of the resolvent of the Volterra equation with a nonintegrable difference kernel”, Differential Equations, 39:6 (2003), 892  mathnet  crossref  mathscinet  zmath  isi  scopus  scopus
    8. Z. B. Tsalyuk, S. S. Chistokletova, “Asymptotic behavior of solutions of Volterra–Hammerstein equations”, Russian Math. (Iz. VUZ), 46:6 (2002), 76–79  mathnet  mathscinet  zmath  elib
    9. Z. B. Tsalyuk, “The structure of the resolvent of a system of renewal equations with a difference kernel”, Russian Math. (Iz. VUZ), 45:6 (2001), 68–76  mathnet  mathscinet  zmath
    10. Z. B. Tsalyuk, “Asymptotic structure of the resolvent of an unstable Volterra equation with a difference kernel”, Russian Math. (Iz. VUZ), 44:4 (2000), 48–53  mathnet  mathscinet  zmath
    Citing articles in Google Scholar: Russian citations, English citations
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