Solvability conditions for the Neumann problem for the homogeneous polyharmonic equation

被引：19

作者：

Karachik, V. V. ^{[1
]}

机构：

[1] South Ural State Univ, Chelyabinsk, Russia

来源：

DIFFERENTIAL EQUATIONS | 2014年 / 50卷 / 11期

关键词：

Dirichlet Problem; Neumann Problem; Solvability Condition; Polynomial Solution; Biharmonic Equation;

D O I：

10.1134/S0012266114110032

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We obtain solvability conditions for the Neumann problem for the homogeneous polyharmonic equation in the unit ball. We study the arithmetic triangle that arises in these conditions. For the elements of that triangle, we obtain recursion relations similar to the relations for the Pascal, Euler, and Stirling triangles. We establish a relationship between the Neumann problem and the Dirichlet problem.

引用

页码：1449 / 1456

页数：8

共 50 条

[1] Solvability conditions for the Neumann problem for the homogeneous polyharmonic equation
V. V. Karachik
[J]. Differential Equations, 2014, 50 : 1449 - 1456
[2] On solvability conditions for the Neumann problem for a polyharmonic equation in the unit ball
Karachik V.V.
[J]. Karachik, V. V. (karachik@susu.ru), 1600, Izdatel'stvo Nauka (08): : 63 - 75
[3] On solvability of the Neumann boundary value problem for a non-homogeneous polyharmonic equation in a ball
Batirkhan K Turmetov
Ravshan R Ashurov
[J]. Boundary Value Problems, 2013
[4] On solvability of the Neumann boundary value problem for a non-homogeneous polyharmonic equation in a ball
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Ashurov, Ravshan R.
[J]. BOUNDARY VALUE PROBLEMS, 2013,
[5] Sufficient Conditions for Solvability of One Class of Neumann-Type Problems for the Polyharmonic Equation
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[J]. COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 2021, 61 (08) : 1276 - 1288
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[J]. Computational Mathematics and Mathematical Physics, 2021, 61 : 1276 - 1288
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[J]. DIFFERENTIAL EQUATIONS, 2018, 54 (05) : 648 - 657
[9] Riquier-Neumann Problem for the Polyharmonic Equation in a Ball
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[J]. MATHEMATICS, 2023, 11 (04)
[10] Solvability of the Neumann problem for a Sobolev pseudoparabolic equation
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[J]. Computational Mathematics and Mathematical Physics, 2006, 46 (7) : 1207 - 1215

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