Geodesic
The Behavior of Solutions of the Nonlinear Biharmonic Equation in an Unbounded Domain
Matematičeskie zametki, Tome 95 (2014) no. 2, pp. 248-256.

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

Periodic (in one variable) solutions in the half-plane of the two-dimensional nonlinear biharmonic equation with exponential nonlinearity on the right-hand side are considered. The power-law and logarithmic asymptotics of the solutions at infinity are obtained.
Keywords: nonlinear biharmonic equation, semilinear elliptic equation, the Laplace operator, Poincaré inequality. 
@article{MZM_2014_95_2_a7,
     author = {A. V. Neklyudov},
     title = {The {Behavior} of {Solutions} of the {Nonlinear} {Biharmonic} {Equation} in an {Unbounded} {Domain}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {248--256},
     publisher = {mathdoc},
     volume = {95},
     number = {2},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2014_95_2_a7/}
}
TY  - JOUR
AU  - A. V. Neklyudov
TI  - The Behavior of Solutions of the Nonlinear Biharmonic Equation in an Unbounded Domain
JO  - Matematičeskie zametki
PY  - 2014
SP  - 248
EP  - 256
VL  - 95
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2014_95_2_a7/
LA  - ru
ID  - MZM_2014_95_2_a7
ER  - 
%0 Journal Article
%A A. V. Neklyudov
%T The Behavior of Solutions of the Nonlinear Biharmonic Equation in an Unbounded Domain
%J Matematičeskie zametki
%D 2014
%P 248-256
%V 95
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2014_95_2_a7/
%G ru
%F MZM_2014_95_2_a7
A. V. Neklyudov. The Behavior of Solutions of the Nonlinear Biharmonic Equation in an Unbounded Domain. Matematičeskie zametki, Tome 95 (2014) no. 2, pp. 248-256. http://geodesic.mathdoc.fr/item/MZM_2014_95_2_a7/

[1] I. N. Vekua, “O nekotorykh svoistvakh reshenii uravneniya Gaussa”, Sbornik statei. Posvyaschaetsya akademiku Ivanu Matveevichu Vinogradovu k ego semidesyatiletiyu, Tr. MIAN SSSR, 64, Izd-vo AN SSSR, M., 1961, 5–8 | MR | Zbl

[2] O. A. Oleinik, “Ob uravnenii $\Delta u+k(x)e^u=0$”, UMN, 33:2 (1978), 203–204 | MR | Zbl

[3] I. Kametaka, O. A. Oleinik, “Ob asimptoticheskikh svoistvakh i neobkhodimykh usloviyakh suschestvovaniya reshenii nelineinykh ellipticheskikh uravnenii vtorogo poryadka”, Matem. sb., 107:4 (1978), 572–600 | MR | Zbl

[4] J. N. Flavin, R. J. Knops, L. E. Payne, “Asymptotic behavior of solutions to semi-linear elliptic equations on the half-cylinder”, Z. Angew. Math. Phys., 43:3 (1992), 405–421 | DOI | MR | Zbl

[5] V. A. Kondratev, O. A. Oleinik, “Ob asimptotike reshenii nelineinykh ellipticheskikh uravnenii”, UMN, 48:4 (1993), 184–185

[6] O. A. Oleinik, Some Asymptotic Problems in the Theory of Partial Differential Equations, Lezioni Lincee, Cambridge Univ. Press, Cambridge, 1996 | MR | Zbl

[7] A. I. Nasrullaev, “Ob asimptotike reshenii zadachi Neimana dlya uravneniya $\Delta u-e^u=0$ v polubeskonechnom tsilindre”, UMN, 50:3 (1995), 161–162 | MR | Zbl

[8] A. I. Nasrullaev, “Ob odnom klase nelineinykh uravnenii v neogranichennykh oblastyakh”, UMN, 51:5 (1996), 160–161 | DOI

[9] A. V. Neklyudov, “Povedenie reshenii polulineinogo ellipticheskogo uravneniya vtorogo poryadka vida $Lu=e^u$ v beskonechnom tsilindre”, Matem. zametki, 85:3 (2009), 408–420 | DOI | MR | Zbl

[10] O. A. Oleinik, G. A. Iosifyan, “O povedenii na beskonechnosti reshenii ellipticheskikh uravnenii vtorogo poryadka v oblastyakh s nekompaktnoi granitsei”, Matem. sb., 112:4 (1980), 588–610 | MR | Zbl

[11] A. V. Neklyudov, “O zadache Neimana dlya divergentnykh ellipticheskikh uravnenii vysokogo poryadka v neogranichennoi oblasti, blizkoi k tsilindru”, Tr. sem. im. I. G. Petrovskogo, 16 (1991), 191–217