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Izv. Vyssh. Uchebn. Zaved. Mat., 2014, Number 7, Pages 15–29 (Mi ivm8908)  

This article is cited in 5 scientific papers (total in 5 papers)

On solvability of some boundary value problems for polyharmonic equation with Hadamard–Marchaud boundary operator

A. E. Bekaevaa, V. V. Karachikb, B. Kh. Turmetova

a Chair of Mathematics, International Kazakh–Turkish University, 2 Esimkhan Ave., Turkestan, 161200 Republic of Kazakhstan
b Chair of Mathematical Analysis, Southern-Ural State University, 76 Lenin Ave., Chelyabinsk, 454080 Russia

Abstract: We investigate solvability conditions of some nonclassical boundary-value problems for the polyharmonic equation. In the capacity of boundary operators we consider fractional differential operators in the sense of Hadamard–Marchaud. Considered problems are generalize the known Dirichlet and Neumann boundary-value problems on boundary operators of fractional type.

Keywords: polyharmonic equation, fractional differential operators, Hadamard–Marchaud operators, Dirichlet and Neumann boundary-value problems.

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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2014, 58:7, 11–24

Document Type: Article
UDC: 517.95
Received: 16.01.2013

Citation: A. E. Bekaeva, V. V. Karachik, B. Kh. Turmetov, “On solvability of some boundary value problems for polyharmonic equation with Hadamard–Marchaud boundary operator”, Izv. Vyssh. Uchebn. Zaved. Mat., 2014, no. 7, 15–29; Russian Math. (Iz. VUZ), 58:7 (2014), 11–24

Citation in format AMSBIB
\Bibitem{BekKarTur14}
\by A.~E.~Bekaeva, V.~V.~Karachik, B.~Kh.~Turmetov
\paper On solvability of some boundary value problems for polyharmonic equation with Hadamard--Marchaud boundary operator
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2014
\issue 7
\pages 15--29
\mathnet{http://mi.mathnet.ru/ivm8908}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2014
\vol 58
\issue 7
\pages 11--24
\crossref{https://doi.org/10.3103/S1066369X14070020}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84903691263}


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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. Sadybekov M.A., Turmetov B.Kh., Muratbekova M.A., “on Solvability of Some Nonlocal Boundary Value Problems With the Hadamard Boundary Operator”, International Conference on Analysis and Applied Mathematics (ICAAM 2014), AIP Conference Proceedings, 1611, eds. Ashyralyev A., Malkowsky E., Amer Inst Physics, 2014, 266–270  crossref  mathscinet  isi
    2. B. Kh. Turmetov, “On solvability of a boundary value problem for an inhomogeneous polyharmonic equation with a fractional order boundary operator”, Ufa Math. J., 8:3 (2016), 155–170  mathnet  crossref  mathscinet  isi  elib
    3. B. Turmetov, M. Koshanova, K. Usmanov, “Solvability of boundary-value problems for Poisson equations with Hadamard type boundary operator”, Electron. J. Differ. Equ., 2016, 161  isi
    4. V. V. Karachik, S. K. Massanov, B. Kh. Turmetov, “On solvability of some boundary value problems for a biharmonic equation with periodic conditions”, International Conference on Analysis and Applied Mathematics ICAAM 2016, AIP Conf. Proc., 1759, eds. A. Ashyralyev, A. Lukashov, Amer. Inst. Phys., 2016, 020118  crossref  isi
    5. B. Kh. Turmetov, “On the solvability of some boundary value problems for the inhomogeneous polyharmonic equation with boundary operators of the Hadamard type”, Differ. Equ., 53:3 (2017), 333–344  crossref  isi  elib
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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