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Matematicheskie Zametki, 2014, Volume 96, Issue 5, Pages 773–789
DOI: https://doi.org/10.4213/mzm10220 (Mi mzm10220) 		 
This article is cited in 24 scientific papers (total in 24 papers)

On the Solvability of a Class of Volterra Operator Equations of the First Kind with Piecewise Continuous Kernels

N. A. Sidorova, D. N. Sidorovabc

a Irkutsk State University
b L. A. Melentiev Energy Systems Institute, Siberian Branch of the Russian Academy of Sciences
c National Research Irkutsk State Technical University
Full-text PDF (570 kB) Citations (24)
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DOI: https://doi.org/10.4213/mzm10220
Abstract: We obtain sufficient conditions for the existence and uniqueness of continuous solutions of Volterra operator equations of the first kind with piecewise determined kernels. For the case in which the solution is not unique, we prove existence theorems for the parametric families of solutions and present their asymptotics in the form of logarithmic polynomials.
Keywords: Volterra operator equation, Banach space, asymptotic approximation, successive approximation method, Fredholm point, Fredholm operator, Jordan set.
Received: 09.10.2012
Revised: 30.11.2013
English version:
Mathematical Notes, 2014, Volume 96, Issue 5, Pages 811–826
DOI: https://doi.org/10.1134/S0001434614110170
Bibliographic databases:
Document Type: Article
UDC: 517.968.22
Language: Russian
Citation: N. A. Sidorov, D. N. Sidorov, “On the Solvability of a Class of Volterra Operator Equations of the First Kind with Piecewise Continuous Kernels”, Mat. Zametki, 96:5 (2014), 773–789; Math. Notes, 96:5 (2014), 811–826
Citation in format AMSBIB
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    • This publication is cited in the following 24 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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