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This article is cited in 9 scientific papers (total in 9 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:
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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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Linking options:
http://mi.mathnet.ru/eng/mz10114https://doi.org/10.4213/mzm10114 http://mi.mathnet.ru/eng/mz/v96/i2/p228
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This publication is cited in the following articles:
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E. Yu. Chistyakov, “O resheniyakh volnovogo uravneniya s mladshim chlenom”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 7:4 (2015), 74–76
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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
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V. V. Karachik, “A Neumann-type problem for the biharmonic equation”, Siberian Adv. Math., 27:2 (2017), 103–118
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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
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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
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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
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V. V. Karachik, “Integralnye tozhdestva na sfere dlya normalnykh proizvodnykh poligarmonicheskikh funktsii”, Sib. elektron. matem. izv., 14 (2017), 533–551
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Karachik V.V. Turmetov B.Kh., “on a Class of Neumann Type Problems For Polyharmonic Equation”, AIP Conference Proceedings, 2172, ed. Pasheva V. Popivanov N. Venkov G., Amer Inst Physics, 2019, 030002
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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
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