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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.], 2012, Issue 4(29), Pages 17–25 (Mi vsgtu1123)  

This article is cited in 17 scientific papers (total in 17 papers)

Differential Equations

Problem with shift for the third-order equation with discontinuous coefficients

O. A. Repinab, S. K. Kumykovac

a Samara State Technical University, Samara, Russia
b Samara State Economic University, Samara, Russia
c Kabardino-Balkar State University, Nalchik, Russia

Abstract: The unique solvability of boundary value problem with Saigo operators for the third-order equation with multiple characteristics was investigated. The uniqueness theorem with constraints of inequality type on the known functions and different orders of generalized fractional integro-differentiation was proved. The existence of solution is equivalently reduced to the solvability of Fredholm integral equation of the second kind.

Keywords: boundary value problem, Gauss hypergeometric function, operators of fractional order, Fredholm equation

DOI: https://doi.org/10.14498/vsgtu1123

Full text: PDF file (177 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
References: PDF file   HTML file

Bibliographic databases:

UDC: 517.956.6+517.968.23
MSC: Primary 35M12; Secondary 26A33, 33C05
Original article submitted 17/X/2012
revision submitted – 16/XI/2012

Citation: O. A. Repin, S. K. Kumykova, “Problem with shift for the third-order equation with discontinuous coefficients”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 4(29) (2012), 17–25

Citation in format AMSBIB
\Bibitem{RepKum12}
\by O.~A.~Repin, S.~K.~Kumykova
\paper Problem with shift for the third-order equation with discontinuous coefficients
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2012
\vol 4(29)
\pages 17--25
\mathnet{http://mi.mathnet.ru/vsgtu1123}
\crossref{https://doi.org/10.14498/vsgtu1123}


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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. F. B. Nakhusheva, “Nelokalnaya zadacha dlya nagruzhennogo uravneniya tretego poryadka s kratnymi kharakteristikami”, Sovremennye naukoemkie tekhnologii, 2013, no. 12, 83–86  elib
    2. F. A. Karova, “Zadacha so smescheniem dlya uravneniya tretego poryadka smeshannogo tipa”, Uspekhi sovremennogo estestvoznaniya, 2014, no. 1, 60–62  elib
    3. T. K. Yuldashev, “Obratnaya zadacha dlya odnogo integro-differentsialnogo uravneniya Fredgolma v chastnykh proizvodnykh tretego poryadka”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 1(34) (2014), 56–65  mathnet  crossref  zmath  elib
    4. Zh. A. Balkizov, “Analog zadachi Trikomi dlya uravneniya parabolo-giperbolicheskogo tipa tretego poryadka s operatorom Gellerstedta v oblasti giperbolichnosti”, Doklady Adygskoi (Cherkesskoi) Mezhdunarodnoi akademii nauk, 16:2 (2014), 20–27  elib
    5. T. K. Yuldashev, “Dvoinaya obratnaya zadacha dlya integro-differentsialnogo uravneniya Fredgolma ellipticheskogo tipa”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 2(35) (2014), 39–49  mathnet  crossref  zmath
    6. Zh. A. Balkizov, “Nelokalnaya kraevaya zadacha dlya uravneniya parabolo-giperbolicheskogo tipa tretego poryadka s operatorom Gellerstedta v oblasti giperbolichnosti”, Uravneniya smeshannogo tipa, rodstvennye problemy analiza i informatiki, Tretii Mezhdunarodnyi Rossiisko-Kazakhskii simpozium, OOO “Redaktsiya zhurnala Elbrus”, Nalchik, 2014, 47–49  elib
    7. O. A. Repin, S. K. Kumykova, “Boundary-value problem with Saigo operators for mixed type equation of the third order with multiple characteristics”, Russian Math. (Iz. VUZ), 59:7 (2015), 44–51  mathnet  crossref
    8. T. K. Yuldashev, “On Fredholm partial integro-differential equation of the third order”, Russian Math. (Iz. VUZ), 59:9 (2015), 62–66  mathnet  crossref
    9. O. A. Repin, S. K. Kumykova, “On a nonlocal problem for a third-order equation of mixed type with multiple characteristics”, Differential Equations, 51:6 (2015), 767–775  crossref  crossref  mathscinet  zmath  isi  elib  elib  scopus
    10. Zh. A. Balkizov, “Nelokalnaya kraevaya zadacha dlya modelnogo uravneniya parabolo-giperbolicheskogo tipa tretego poryadka”, Doklady Adygskoi (Cherkesskoi) Mezhdunarodnoi akademii nauk, 17:4 (2015), 9–20  elib
    11. O. A. Repin, S. K. Kumykova, “Vnutrennekraevaya zadacha s operatorami Rimana–Liuvillya dlya uravneniya smeshannogo tipa tretego poryadka”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 20:1 (2016), 43–53  mathnet  crossref  zmath  elib
    12. T. K. Yuldashev, “Obratnaya zadacha dlya integro-differentsialnogo uravneniya Fredgolma tretego poryadka s vyrozhdennym yadrom”, Vladikavk. matem. zhurn., 18:2 (2016), 76–85  mathnet
    13. T. K. Yuldashev, K. Kh. Shabadikov, “Kvazilineinoe integro-differentsialnoe uravnenie psevdoparabolicheskogo tipa s vyrozhdennym yadrom i integralnym usloviem”, Zhurnal SVMO, 18:4 (2016), 76–88  mathnet  elib
    14. Zh. A. Balkizov, “Dirichlet boundary value problem for a third order parabolic-hyperbolic equation with degenerating type and order in the hyperbolicity domain”, Ufa Math. J., 9:2 (2017), 25–39  mathnet  crossref  isi  elib
    15. Zh. A. Balkizov, “Kraevaya zadacha so smescheniem dlya modelnogo uravneniya parabolo-giperbolicheskogo tipa tretego poryadka”, Vestnik KRAUNTs. Fiz.-mat. nauki, 2018, no. 3(23), 19–26  mathnet  crossref  elib
    16. Zh. A. Balkizov, “Nelokalnaya kraevaya zadacha dlya uravneniya parabolo-giperbolicheskogo tipa tretego poryadka s vyrozhdeniem tipa i poryadka v oblasti ego giperbolichnosti”, Materialy mezhdunarodnoi nauchnoi konferentsii «Aktualnye problemy prikladnoi matematiki i fiziki» Kabardino-Balkariya, Nalchik, 17–21 maya 2017 g., Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 149, VINITI RAN, M., 2018, 14–24  mathnet  mathscinet
    17. O. A. Repin, “Nelokalnaya zadacha s operatorami Saigo dlya uravneniya smeshannogo tipa tretego poryadka”, Izv. vuzov. Matem., 2019, no. 1, 63–68  mathnet  crossref
  • Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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