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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]:
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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2017, Volume 21, Number 2, Pages 236–248 (Mi vsgtu1515)  

This article is cited in 3 scientific papers (total in 3 papers)

Differential Equations and Mathematical Physics

A Construction of analog of Fredgolm theorems for one class of first order model integro-differential equation with logarithmic singularity in the kernel

S. K. Zaripov

Tajik National University, Dushanbe, 734025, Tajikistan

Abstract: The integral representations of the solution manifold for one class of the first order model integro-differential equation with logarithmic singularity in the kernel are constructed using arbitrary constants. The cases when the given integro-differential equation has unique solution are found. The analogue of Fredholm theorem is built for given integro-differential equation. The method of solving this problem can be used for the solving of higher order model and non-model integro-differential equations with singular coefficients.

Keywords: integro-differential equation, boundary singular points, manifold solution, integral representation, characteristic equation

DOI: https://doi.org/10.14498/vsgtu1515

Full text: PDF file (623 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
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Bibliographic databases:

Document Type: Article
UDC: 517.968.73
MSC: 45J05, 34K05, 34K30
Received: October 20, 2016
Revised: March 14, 2017
Accepted: June 12, 2017
First online: July 9, 2017

Citation: S. K. Zaripov, “A Construction of analog of Fredgolm theorems for one class of first order model integro-differential equation with logarithmic singularity in the kernel”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 21:2 (2017), 236–248

Citation in format AMSBIB
\Bibitem{Zar17}
\by S.~K.~Zaripov
\paper A Construction of analog of Fredgolm theorems for one class of first order
model integro-differential equation with logarithmic singularity in the kernel
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2017
\vol 21
\issue 2
\pages 236--248
\mathnet{http://mi.mathnet.ru/vsgtu1515}
\crossref{https://doi.org/10.14498/vsgtu1515}
\zmath{https://zbmath.org/?q=an:06964671}
\elib{http://elibrary.ru/item.asp?id=30039926}


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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. T. K. Yuldashev, “Obobschennaya razreshimost nelokalnoi zadachi dlya integro-differentsialnogo uravneniya chetvertogo poryadka s vyrozhdennym yadrom”, Vestnik Oshskogo gosudarstvennogo universiteta, 2017, no. 4, 238–249  elib
    2. S. K. Zaripov, “Ob odnom klasse modelnykh integro-differentsialnykh uravnenii pervogo poryadka so stepennoi osobennostyu v yadre”, Vestnik Tadzhikskogo natsionalnogo universiteta. Seriya estestvennykh nauk, 2018, no. 1, 16–21  elib
    3. S. K. Zaripov, “Issledovanie odnogo klassa sopryazhennogo singulyarnogo integro-differentsialnogo uravneniya”, Vestnik Tadzhikskogo natsionalnogo universiteta. Seriya estestvennykh nauk, 2018, no. 2, 21–28  elib
  • Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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