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Ufimsk. Mat. Zh., 2010, Volume 2, Issue 2, Pages 41–52 (Mi ufa50)  

This article is cited in 20 scientific papers (total in 20 papers)

Necessary and sufficient conditions of resolvability boundary problems for non-uniform polyharmonis equations in ball

B. E. Kanguzhina, B. D. Koshanovb

a Al-Farabi Kazakh National University, Almaty, Kazakhstan
b Institute of Mathematics, Ministry of Education and Science, Republic of Kazakhstan, Almaty, Kazakhstan

Abstract: In the work are different boundary value problems for nonhomogeneous polyharmonic equations in a sphere of an arbitrary dimension. Also is to construct in the explicit form the Green function for Dirichlet problem for nonhomogeneous polyharmonic equation in a sphere.

Keywords: Dirichlet problem, Neumann's problem, the polyharmonics equation.

Full text: PDF file (437 kB)
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Document Type: Article
UDC: 517.95
Received: 08.02.2010

Citation: B. E. Kanguzhin, B. D. Koshanov, “Necessary and sufficient conditions of resolvability boundary problems for non-uniform polyharmonis equations in ball”, Ufimsk. Mat. Zh., 2:2 (2010), 41–52

Citation in format AMSBIB
\Bibitem{KanKos10}
\by B.~E.~Kanguzhin, B.~D.~Koshanov
\paper Necessary and sufficient conditions of resolvability boundary problems for non-uniform polyharmonis equations in ball
\jour Ufimsk. Mat. Zh.
\yr 2010
\vol 2
\issue 2
\pages 41--52
\mathnet{http://mi.mathnet.ru/ufa50}
\zmath{https://zbmath.org/?q=an:1240.35141}
\elib{http://elibrary.ru/item.asp?id=15253177}


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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. A. E. Bekaeva, V. V. Karachik, B. Kh. Turmetov, “On solvability of some boundary value problems for polyharmonic equation with Hadamard–Marchaud boundary operator”, Russian Math. (Iz. VUZ), 58:7 (2014), 11–24  mathnet  crossref
    2. V. V. Karachik, “Construction of polynomial solutions to the Dirichlet problem for the polyharmonic equation in a ball”, Comput. Math. Math. Phys., 54:7 (2014), 1122–1143  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    3. V. V. Karachik, “Reshenie zadachi Dirikhle dlya poligarmonicheskogo uravneniya v share”, Vestn. Natsionalnogo issledovatelskogo yadernogo un-ta MIFI, 3:6 (2014), 649–655  elib
    4. V. V. Karachik, “Postroenie resheniya zadachi Dirikhle dlya poligarmonicheskogo uravneniya v share s polinomialnymi dannymi”, Sistemy kompyuternoi matematiki i ikh prilozheniya, 2014, no. 15, 153–155  elib
    5. Berdyshev A.S., Cabada A., Turmetov B.Kh., “On Solvability of a Boundary Value Problem For a Nonhomogeneous Biharmonic Equation With a Boundary Operator of a Fractional Order”, Acta Math. Sci., 34:6 (2014), 1695–1706  crossref  mathscinet  zmath  isi
    6. Karachik V.V., “Solution of the Dirichlet Problem With Polynomial Data For the Polyharmonic Equation in a Ball”, Differ. Equ., 51:8 (2015), 1033–1042  crossref  mathscinet  zmath  isi  scopus
    7. Georgievskii D.V., “The Galerkin Tensor Operator, Reduction to Tetraharmonic Equations, and Their Fundamental Solutions”, Dokl. Phys., 60:8 (2015), 364–367  crossref  mathscinet  isi  scopus
    8. Berdyshev A.S., Cabada A., Turmetov B.Kh., “On Solvability of Some Boundary Value Problem For Polyharmonic Equation With Boundary Operator of a Fractional Order”, Appl. Math. Model., 39:15 (2015), 4548–4569  crossref  mathscinet  isi  scopus
    9. Koshanov B.D., Koshanova M.D., “On the Representation of the Green Function of the Dirichlet Problem and Their Properties For the Polyharmonic Equations”, AIP Conference Proceedings, 1676, eds. Ashyralyev A., Malkowsky E., Lukashov A., Basar F., Amer Inst Physics, 2015, 020020  crossref  isi
    10. 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
    11. V. V. Karachik, “A Neumann-type problem for the biharmonic equation”, Siberian Adv. Math., 27:2 (2017), 103–118  mathnet  crossref  crossref  elib
    12. Turmetov B., “On Some Boundary Value Problems For Nonhomogenous Polyharmonic Equation With Boundary Operators of Fractional Order”, Acta Math. Sci., 36:3 (2016), 831–846  crossref  mathscinet  zmath  isi
    13. Turmetov B.Kh., Karachik V.V., “About One Boundary Value Problem For the Biharmonic Equation”, AIP Conference Proceedings, 1789, eds. Pasheva V., Popivanov N., Venkov G., Amer Inst Physics, 2016, UNSP 040015  crossref  isi  scopus
    14. I. A. Gulyaschikh, “Razreshimost odnoi zadachi tipa Neimana dlya trigarmonicheskogo uravneniya v share”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 9:3 (2017), 5–12  mathnet  crossref  elib
    15. V. V. Karachik, “Zadacha tipa Neimana dlya poligarmonicheskogo uravneniya v share”, Chelyab. fiz.-matem. zhurn., 2:4 (2017), 420–429  mathnet  mathscinet  elib
    16. Turmetov B.Kh., “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  mathscinet  zmath  isi  scopus
    17. Koshanov B.D., Adilbekov E.N., Duysen E., “The Dimension of the Space Solutions of the Dirichlet Problem For the Poisson and Biharmonic Equations in Unbounded Domains - i”, News Natl. Acad. Sci. Rep. Kazakhstan-Ser. Phys.-Math., 2:312 (2017), 116–125  isi
    18. Koshanov B.D., Adilbekov E.N., Duysen E., “The Dimension of the Space Solutions of the Dirichlet Problem For the Poisson and Biharmonic Equations in Unbounded Domains - II”, News Natl. Acad. Sci. Rep. Kazakhstan-Ser. Phys.-Math., 2:312 (2017), 126–131  isi
    19. Koshanov B.D., Smatova G.D., “On Correct Restrictions of Bi-Laplace Operator and Their Properties”, AIP Conference Proceedings, 1880, eds. Kalmenov T., Sadybekov M., Amer Inst Physics, 2017, UNSP 050016  crossref  isi  scopus
    20. Dubey Sh., Kumar A., Mishra M.M., “Polyharmonic Neumann Andmixed Boundary Value Problems in the Heisenberg Group H-N”, Complex Var. Elliptic Equ., 62:10, SI (2017), 1506–1518  crossref  mathscinet  zmath  isi  scopus
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