On Fredholm Solvability and on the Index of the Generalized Neumann Problem for an Elliptic Equation of High Order on a Plane

被引：0

作者：

Koshanov, Bakytbek ^{[1
]}

Bakytbek, Maksat ^{[2
]}

机构：

[1] Al Farabi Kazakh Natl Univ, Int Univ Informat Technol, Alma Ata, Kazakhstan

[2] Kazakh Acad Transport & Commun, Alma Ata, Kazakhstan

来源：

EXTENDED ABSTRACTS MWCAPDE 2023 | 2024年 / 1卷

关键词：

PARTIAL-DIFFERENTIAL EQUATIONS; GREEN-FUNCTION REPRESENTATION; BOUNDARY-VALUE PROBLEM; DIRICHLET PROBLEM;

D O I：

10.1007/978-3-031-41665-1_19

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we investigate the Fredholm solvability of the generalized Neumann problem for a high-order elliptic equation on a plane. The equivalence of the solvability conditions of the generalized Neumann problem to the complementarity condition (Shapiro-Lopatinskii condition) is proved. The formula for the index of the specified problem in the class C-2l,C-mu (<(D) over bar>) is calculated.

引用

页码：167 / 176

页数：10

共 50 条

[41] On the Plane Neumann Problem with Generalized Boundary Conditions
A. V. Setukha
Differential Equations, 2002, 38 : 1246 - 1259
[42] On solvability conditions for the Neumann problem for a polyharmonic equation in the unit ball
Karachik V.V.
Karachik, V. V. (karachik@susu.ru), 1600, Izdatel'stvo Nauka (08): : 63 - 75
[43] Solvability of the Neumann Boundary Value Problem for the Polyharmonic Equation in a Ball
Karachik, V.
LOBACHEVSKII JOURNAL OF MATHEMATICS, 2024, 45 (08) : 3559 - 3571
[44] On the solvability of a boundary-value problem for an elliptic equation
Il'in, A. M.
Rep'evskii, S. V.
MATHEMATICAL NOTES, 2012, 92 (1-2) : 197 - 204
[45] On the solvability of a boundary-value problem for an elliptic equation
A. M. Il’in
S. V. Rep’evskii
Mathematical Notes, 2012, 92 : 197 - 204
[46] On the neumann problem for the Helmholtz equation in a plane angle
Zhevandrov, P
Merzon, A
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2000, 23 (16) : 1401 - 1446
[47] ONE PROBLEM FOR AN ELLIPTIC EQUATION AND THE CONDITIONS OF ITS SOLVABILITY
SHAMILOV, AK
DOKLADY AKADEMII NAUK SSSR, 1981, 261 (04): : 820 - 824
[48] ON THE SOLVABILITY OF ELLIPTIC PROBLEM IN R WITH SUPERCRITICAL INDEX OF NONLINEARITY
POKHOZHAEV, SI
DOKLADY AKADEMII NAUK SSSR, 1990, 313 (06): : 1356 - 1360
[49] On the solvability of an initial boundary problem for a high even order degenerate equation
Urinov, A. K.
Oripov, D. D.
VESTNIK SAMARSKOGO GOSUDARSTVENNOGO TEKHNICHESKOGO UNIVERSITETA-SERIYA-FIZIKO-MATEMATICHESKIYE NAUKI, 2023, 27 (04): : 621 - 644
[50] On the solvability of the higher order elliptic boundary value problem
Agarwal, Ravi P.
Chen, Jinhai
APPLIED MATHEMATICS LETTERS, 2009, 22 (08) : 1195 - 1199

← 1 2 3 4 5 →