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Mat. Zametki, 2014, Volume 96, Issue 2, Pages 228–238 (Mi mz10114)  

This article is cited in 8 scientific papers (total in 8 papers)

On the Arithmetic Triangle Arising from the Solvability Conditions for the Neumann Problem

V. V. Karachik

South Ural State University, Chelyabinsk

Abstract: We study the arithmetic triangle arising from the solvability conditions for the Neumann problem for the polyharmonic equation in the unit ball. Recurrence relations for the elements of this triangle are obtained.

Keywords: Neumann problem, polyharmonic equation, arithmetic triangle, Vandermond determinant.

DOI: https://doi.org/10.4213/mzm10114

Full text: PDF file (464 kB)
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English version:
Mathematical Notes, 2014, 96:2, 217–227

Bibliographic databases:

UDC: 512.643.2+517.953
Received: 04.07.2012
Revised: 12.08.2013

Citation: V. V. Karachik, “On the Arithmetic Triangle Arising from the Solvability Conditions for the Neumann Problem”, Mat. Zametki, 96:2 (2014), 228–238; Math. Notes, 96:2 (2014), 217–227

Citation in format AMSBIB
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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. E. Yu. Chistyakov, “O resheniyakh volnovogo uravneniya s mladshim chlenom”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 7:4 (2015), 74–76  mathnet  crossref  elib
    2. A. S. Berdyshev, A. Cabada, B. Kh. Turmetov, “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  elib  scopus
    3. V. V. Karachik, “A Neumann-type problem for the biharmonic equation”, Siberian Adv. Math., 27:2 (2017), 103–118  mathnet  crossref  crossref  elib
    4. B. Turmetov, “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  elib  scopus
    5. B. Kh. Turmetov, V. V. Karachik, “About one boundary value problem for the biharmonic equation”, Applications of Mathematics in Engineering and Economics (AMEE'16), AIP Conference Proceedings, 1789, eds. V. Pasheva, N. Popivanov, G. Venkov, Amer Inst Physics, 2016, UNSP 040015  crossref  isi  scopus
    6. Sh. Dubey, A. Kumar, M. M. Mishra, “Polyharmonic Neumann andmixed boundary value problems in the Heisenberg group $\Bbb H_n$”, Complex Var. Elliptic Equ., 62:9, SI (2017), 1506–1518  crossref  mathscinet  zmath  isi  scopus
    7. V. V. Karachik, “Integralnye tozhdestva na sfere dlya normalnykh proizvodnykh poligarmonicheskikh funktsii”, Sib. elektron. matem. izv., 14 (2017), 533–551  mathnet  crossref  mathscinet  zmath
    8. V. V. Karachik, “Usloviya razreshimosti zadachi Neimana $\mathcal{N}_2$ dlya poligarmonicheskogo uravneniya v share”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 12:2 (2020), 13–20  mathnet  crossref
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