Neumann type problem for polyharmonic equation in a ball
Čelâbinskij fiziko-matematičeskij žurnal, Tome 2 (2017) no. 4, pp. 420-429.

Voir la notice de l'article provenant de la source Math-Net.Ru

The necessary and sufficient solvability condition for a Neumann-type boundary value problem for nonhomogeneous polyharmonic equation in the unit ball are obtained.
Keywords: Requier problem, Neumann problem, polyharmonic equation, solvability condition.
@article{CHFMJ_2017_2_4_a4,
     author = {V. V. Karachik},
     title = {Neumann type problem for polyharmonic equation in a ball},
     journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal},
     pages = {420--429},
     publisher = {mathdoc},
     volume = {2},
     number = {4},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHFMJ_2017_2_4_a4/}
}
TY  - JOUR
AU  - V. V. Karachik
TI  - Neumann type problem for polyharmonic equation in a ball
JO  - Čelâbinskij fiziko-matematičeskij žurnal
PY  - 2017
SP  - 420
EP  - 429
VL  - 2
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CHFMJ_2017_2_4_a4/
LA  - ru
ID  - CHFMJ_2017_2_4_a4
ER  - 
%0 Journal Article
%A V. V. Karachik
%T Neumann type problem for polyharmonic equation in a ball
%J Čelâbinskij fiziko-matematičeskij žurnal
%D 2017
%P 420-429
%V 2
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CHFMJ_2017_2_4_a4/
%G ru
%F CHFMJ_2017_2_4_a4
V. V. Karachik. Neumann type problem for polyharmonic equation in a ball. Čelâbinskij fiziko-matematičeskij žurnal, Tome 2 (2017) no. 4, pp. 420-429. http://geodesic.mathdoc.fr/item/CHFMJ_2017_2_4_a4/

[1] H. C. Grunau, G. Sweers, Polyharmonic boundary value problems. Positivity preserving and nonlinear higher order elliptic equations in bounded domains, Springer, Berlin, 2010, 423 pp.

[2] V. V. Karachik, “Normalized system of functions with respect to the Laplace operator and its applications”, Journal of Mathematical Analysis and Applications, 287:2 (2003), 577–592

[3] V. V. Karachik, M. A. Sadybekov, B. T. Torebek, “Uniqueness of solutions to boundary-value problems for the biharmonic equation in a ball”, Electronic Journal of Differential Equations, 2015:244 (2015), 1–9

[4] V. V. Karachik, B. T. Torebek, “On one mathematical model described by boundary value problem for the biharmonic equation”, Bulletin of the South Ural State University. Ser. Mathematical Modelling, Programming Computer Software, 9:4 (2016), 40–52 (In Russ.)

[5] V.V. Karachik, B.T. Torebek, “On the Dirichlet — Riquier problem for biharmonic equations”, Mathematical Notes, 102:1 (2017), 31–42

[6] V.V. Karachik, “Generalized third boundary value problem for the biharmonic equation”, Differential Equations, 53:6 (2017), 756–765

[7] P. Collet, J. P. Eckmann, Instabilities and Fronts in Extended Systems, Princeton University Press, N. Y., 1980, 195 pp.

[8] I.A. Gulyashikh, “On Neumann problem for polyharmonic equation in the unit ball”, Systems of computer mathematics and their applications, 2015, no. 16, 144–145 (In Russ.)

[9] V.V. Karachik, “Solvability conditions for the Neumann problem for the homogeneous polyharmonic equation”, Differential Equations, 50:11 (2014), 1449–1456

[10] B.E. Kanguzhin, B.D. Koshanov, “Necessary and sufficient conditions of boundary problems solvability for a nonhomogeneous polyharmonic equation in a ball”, Ufa Mathematical Journal, 2:2 (2010), 41–52 (In Russ.)

[11] V.V. Karachik, “A Neumann-type problem for the biharmonic equation”, Siberian Advances in Mathematics, 27:2 (2017), 103–118

[12] B. Turmetov, R. Ashurov, “On solvability of the Neumann boundary value problem for non-homogeneous biharmonic equation”, British Journal of Mathematics and Computer Sciences, 4:4 (2014), 557–571

[13] B. Kh. Turmetov, V. V. Karachik, “About one boundary value problem for the biharmonic equation”, AIP Conference Proceedings, 1789 (2016), 040015-1–040015-6

[14] B.D. Koshanov, A.P. Soldatov, “Boundary value problem with normal derivatives for a higher-order elliptic equation on the plane”, Differential Equations, 52:12 (2016), 1594–1609

[15] V.V. Karachik, “Construction of polynomial solutions to the Dirichlet problem for the polyharmonic equation in a ball”, Computational Mathematics and Mathematical Physics, 54:7 (2014), 1122–1143

[16] I.A. Gulyashikh, “Solvability of one Neumann type problem for 3-harmonic equation in a ball”, Bulletin of the South Ural State University. Series: Mathematics. Mechanics. Physics, 9:3 (2017), 5–12 (In Russ.)

[17] S.L. Sobolev, Introduction to the theory of cubature formulas, Nauka Publ., Moscow, 1974, 808 pp. (In Russ.)

[18] V.V. Karachik, “On an expansion of Almansi type”, Mathematical Notes, 83:3–4 (2008), 335–344

[19] A.V. Bitsadze, Equations of Mathematical Physics, Nauka Publ., Moscow, 1982, 318 pp. (In Russ.)

[20] V.V. Karachik, “On Solvability Conditions for the Neumann Problem for a Polyharmonic Equation in the Unit Ball”, Journal of Applied and Industrial Mathematics, 8:1 (2014), 63–75