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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.], 2016, Volume 20, Number 4, Pages 644–655 (Mi vsgtu1502)  

This article is cited in 1 scientific paper (total in 1 paper)

Differential Equations and Mathematical Physics

An ordinary integro-differential equation with a degenerate kernel and an integral condition

T. K. Yuldashev

M. F. Reshetnev Siberian State Aerospace University, Krasnoyarsk, 660014, Russian Federation

Abstract: We consider the questions of one value solvability of the nonlocal boundary value problem for a nonlinear ordinary integro-differential equation with a degenerate kernel and a reflective argument. The method of the degenerate kernel is developed for the case of considering ordinary integro-differential equation of the first order. After denoting the integro-differential equation is reduced to a system of algebraic equations with complex right-hand side. After some transformation we obtaine the nonlinear functional-integral equation, which one valued solvability is proved by the method of successive approximations combined with the method of compressing mapping. This paper advances the theory of nonlinear integro-differential equations with a degenerate kernel.

Keywords: integro-differential equation, degenerate kernel, reflective argument, integral form condition, one valued solvability.

DOI: https://doi.org/10.14498/vsgtu1502

Full text: PDF file (770 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
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Bibliographic databases:

UDC: 517.968.74
MSC: 34K10, 34K99
Original article submitted 23/VII/2016
revision submitted – 15/X/2016

Citation: T. K. Yuldashev, “An ordinary integro-differential equation with a degenerate kernel and an integral condition”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 20:4 (2016), 644–655

Citation in format AMSBIB
\Bibitem{Yul16}
\by T.~K.~Yuldashev
\paper An ordinary integro-differential equation with~a~degenerate kernel and an integral condition
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2016
\vol 20
\issue 4
\pages 644--655
\mathnet{http://mi.mathnet.ru/vsgtu1502}
\crossref{https://doi.org/10.14498/vsgtu1502}
\zmath{https://zbmath.org/?q=an:06964661}
\elib{http://elibrary.ru/item.asp?id=28862960}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. T. K. Yuldashev, “Obobschennaya razreshimost smeshannoi zadachi dlya nelineinogo integro-differentsialnogo uravneniya vysokogo poryadka s vyrozhdennym yadrom”, Izv. IMI UdGU, 50 (2017), 121–132  mathnet  crossref  elib
  • Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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