Four Boundary Value Problems for a Nonlocal Biharmonic Equation in the Unit Ball

被引：9

作者：

Karachik, Valery ^{[1
]}

Turmetov, Batirkhan ^{[2
]}

Yuan, Hongfen ^{[3
]}

机构：

[1] South Ural State Univ NRU, Dept Math Anal, Chelyabinsk 454080, Russia

[2] Khoja Akhmet Yassawi Int Kazakh Turkish Univ, Dept Math, Turkistan 161200, Kazakhstan

[3] Hebei Univ Engn, Sch Math & Phys, Handan 056038, Peoples R China

来源：

MATHEMATICS | 2022年 / 10卷 / 07期

基金：

中国国家自然科学基金;

关键词：

nonlocal equation; biharmonic equation; Dirichlet problem; Neumann problem; Navier problem; Riquier-Neumann problem; existence and uniqueness; Green's function; 2ND-ORDER DIFFERENTIAL-EQUATION; POLYHARMONIC EQUATION; SOLVABILITY;

D O I：

10.3390/math10071158

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Solvability issues of four boundary value problems for a nonlocal biharmonic equation in the unit ball are investigated. Dirichlet, Neumann, Navier and Riquier-Neumann boundary value problems are studied. For the problems under consideration, existence and uniqueness theorems are proved. Necessary and sufficient conditions for the solvability of all problems are obtained and an integral representations of solutions are given in terms of the corresponding Green's functions.

引用

页数：21

共 34 条

[1] AN INVERSE PROBLEM FOR SPACE AND TIME FRACTIONAL EVOLUTION EQUATIONS WITH AN INVOLUTION PERTURBATION [J].

Ahmad, Bashir ;

Alsaedi, Ahmed ;

Kirane, Mokhtar ;

Tapdigoglu, Ramiz G. .

QUAESTIONES MATHEMATICAE, 2017, 40 (02) :151-160

[2] Analogs of classical boundary value problems for a second-order differential equation with deviating argument [J].

Andreev, AA .

DIFFERENTIAL EQUATIONS, 2004, 40 (08) :1192-1194

[3] Well-Posedness of a Parabolic Equation with Involution [J].

Ashyralyev, Allaberen ;

Sarsenbi, Abdizhahan .

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2017, 38 (10) :1295-1304

[4]

Ashyralyev A, 2015, ELECTRON J DIFFER EQ

[5]

Babbage Ch., 1815, ESSAYS CALCULUS FUNC

[6] Spectral analysis of a differential operator with an involution [J].

Baskakov, Anatoly G. ;

Krishtal, Ilya A. ;

Romanova, Elena Yu. .

JOURNAL OF EVOLUTION EQUATIONS, 2017, 17 (02) :669-684

[7]

Begehr H, 2006, MATEMATICHE, V61, P395

[8] Fourier method in an initial-boundary value problem for a first-order partial differential equation with involution [J].

Burlutskaya, M. Sh ;

Khromov, A. P. .

COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 2011, 51 (12) :2102-2114

[9] On linear differential equations and systems with reflection [J].

Cabada, Alberto ;

Tojo, F. Adrian F. .

APPLIED MATHEMATICS AND COMPUTATION, 2017, 305 :84-102

[10]

Evans L.C., 1998, Graduate studies in mathematics

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