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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.], 2015, Volume 19, Number 4, Pages 736–749 (Mi vsgtu1434)  

This article is cited in 7 scientific papers (total in 7 papers)

Differential Equations and Mathematical Physics

An inverse problem for a nonlinear Fredholm integro-differential equation of fourth order with degenerate kernel

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 inverse problem for a nonlinear partial Fredholm type integro-differential equation of the fourth order with degenerate kernel. The method of degenerate kernel is developed for the case of inverse problem for the considering partial Fredholm type integro-differential equation of the fourth order. After denoting the Fredholm type integro-differential equation is reduced to a system of integral equations. By the aid of differentiating the system of integral equations reduced to the system of differential equations. When a certain imposed condition is fulfilled, the system of differential equations is changed to the system of algebraic equations. For the regular values of spectral parameterthe system of algebraic equations is solved by the Kramer metod. Using the given additional condition the nonlinear Volterra type integral equation of second kind with respect to main unknowing function and the nonlinear Volterra special type integral equation of first kind with respect to restore function are obtained. We use the method of successive approximations combined with the method of compressing maps. Further the restore function is defined. This paper developes the theory of Fredholm integro-differential equations with degenerate kernel.

Keywords: inverse problem, integro-differential equation, Fredholm type equation, degenerate kernel, system of integral equations, one valued solvability

DOI: https://doi.org/10.14498/vsgtu1434

Full text: PDF file (727 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
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Bibliographic databases:

UDC: 517.968.21
MSC: 45B05
Original article submitted 29/IV/2015
revision submitted – 14/VI/2015

Citation: T. K. Yuldashev, “An inverse problem for a nonlinear Fredholm integro-differential equation of fourth order with degenerate kernel”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 19:4 (2015), 736–749

Citation in format AMSBIB
\Bibitem{Yul15}
\by T.~K.~Yuldashev
\paper An inverse problem for a nonlinear Fredholm
integro-differential equation of fourth order with degenerate kernel
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2015
\vol 19
\issue 4
\pages 736--749
\mathnet{http://mi.mathnet.ru/vsgtu1434}
\crossref{https://doi.org/10.14498/vsgtu1434}
\zmath{https://zbmath.org/?q=an:06969191}
\elib{http://elibrary.ru/item.asp?id=25687500}


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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, “Ob odnom smeshannom differentsialnom uravnenii chetvertogo poryadka”, Izv. IMI UdGU, 2016, no. 1(47), 119–128  mathnet  elib
    2. T. K. Yuldashev, “Nonlocal problem for a mixed type differential equation in rectangular domain”, Uch. zapiski EGU, ser. Fizika i Matematika, 2016, no. 3, 70–78  mathnet
    3. T. K. Yuldashev, “Ob odnoi kraevoi zadache dlya trekhmernogo analoga differentsialnogo uravneniya Bussineska”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 158, no. 3, Izd-vo Kazanskogo un-ta, Kazan, 2016, 424–433  mathnet  mathscinet  elib
    4. T. K. Yuldashev, “Obyknovennoe integro-differentsialnoe uravnenie s vyrozhdennym yadrom i integralnym usloviem”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 20:4 (2016), 644–655  mathnet  crossref  zmath  elib
    5. T. K. Yuldashev, “Smeshannoe differentsialnoe uravnenie tipa Bussineska”, Vestnik VolGU. Seriya 1. Matematika. Fizika, 2016, no. 2(33), 13–26  mathnet  crossref
    6. T. K. Yuldashev, “Nelokalnaya kraevaya zadacha dlya neodnorodnogo psevdoparabolicheskogo integro-differentsialnogo uravneniya s vyrozhdennym yadrom”, Vestn. Volgogr. gos. un-ta. Ser. 1, Mat. Fiz., 2017, no. 1(38), 42–54  mathnet  crossref
    7. T. K. Yuldashev, “Ob odnoi nelokalnoi obratnoi zadache dlya nelineinogo integro-differentsialnogo uravneniya Benney-Luke s vyrozhdennym yadrom”, Vestnik TvGU. Seriya: Prikladnaya matematika, 2018, no. 3, 19–41  mathnet  crossref  elib
  • Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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