Geodesic
Behavior at infinity of solutions of second-order nonlinear equations of a~particular class
Matematičeskie zametki, Tome 60 (1996) no. 1, pp. 30-39.

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

Let $\Omega$ be an arbitrary, possibly unbounded, open subset of $\mathbb R^n$, and let $L$ be an elliptic operator of the form $$ L=\sum_{i,j=1}^n \frac\partial{\partial x_i} \biggl(a_{ij}(x)\frac\partial{\partial x_j}\biggr). $$ The behavior at infinity of the solutions of the equation $Lu=f(|u|)\operatorname{sign}u$ in $\Omega$ is studied, where $f$ is a measurable function. In particular, given certain conditions at infinity, the uniqueness theorem for the solution of the first boundary value problem is proved. 
@article{MZM_1996_60_1_a3,
     author = {A. A. Kon'kov},
     title = {Behavior at infinity of solutions of second-order nonlinear equations of a~particular class},
     journal = {Matemati\v{c}eskie zametki},
     pages = {30--39},
     publisher = {mathdoc},
     volume = {60},
     number = {1},
     year = {1996},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1996_60_1_a3/}
}
TY  - JOUR
AU  - A. A. Kon'kov
TI  - Behavior at infinity of solutions of second-order nonlinear equations of a~particular class
JO  - Matematičeskie zametki
PY  - 1996
SP  - 30
EP  - 39
VL  - 60
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_1996_60_1_a3/
LA  - ru
ID  - MZM_1996_60_1_a3
ER  - 
%0 Journal Article
%A A. A. Kon'kov
%T Behavior at infinity of solutions of second-order nonlinear equations of a~particular class
%J Matematičeskie zametki
%D 1996
%P 30-39
%V 60
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_1996_60_1_a3/
%G ru
%F MZM_1996_60_1_a3
A. A. Kon'kov. Behavior at infinity of solutions of second-order nonlinear equations of a~particular class. Matematičeskie zametki, Tome 60 (1996) no. 1, pp. 30-39. http://geodesic.mathdoc.fr/item/MZM_1996_60_1_a3/

[1] Kondratev V. A., Landis E. M., “O kachestvennykh svoistvakh reshenii odnogo nelineinogo uravneniya vtorogo poryadka”, Matem. sb., 135 (177):3 (1988), 346–360 | Zbl

[2] Veron L., “Singular solutions of some nonlinear elliptic equations”, Nonlinear Anal., 5:3 (1981), 225–242 | DOI | MR | Zbl

[3] Veron L., “Comportement asymptotique des solutions d'equations elliptiques semi-linearer dans $\mathbb R^n$”, Ann. Mat. Pura Appl., 127 (1981), 25–50 | DOI | MR | Zbl

[4] Brezis H., Veron L., “Removable singularities for some nonlinear elliptic equations”, Arch. Rational Mech. Anal., 75:1 (1980), 1–6 | DOI | MR | Zbl

[5] Keller J. B., “On solution of $\Delta u=f(u)$”, Comm. Pure Appl. Math., 10:4 (1957), 503–510 | DOI | MR | Zbl

[6] Osserman R., “On the inequality $\Delta u\ge f(u)$”, Pacif. J. Math., 7:4 (1957), 1641–1647 | MR | Zbl

[7] Pokhozhaev S. I., “O kraevoi zadache dlya uravneniya $\Delta u=u^2$”, Dokl. AN SSSR, 140:3 (1961), 518–521

[8] Landis E. M., “Nekotorye voprosy kachestvennoi teorii ellipticheskikh uravnenii vtorogo poryadka”, UMN, 18:1 (1963), 3–62 | MR | Zbl

[9] Gerver M. L., Landis E. M., “Odno obobschenie teoremy o srednem dlya mnogikh peremennykh”, Dokl. AN SSSR, 1962, no. 4, 761–764 | MR | Zbl

[10] Landis E. M., Uravneniya vtorogo poryadka ellipticheskogo i parabolicheskogo tipov, Nauka, M., 1971

[11] Ladyzhenskaya O. A., Uraltseva N. N., Lineinye i kvazilineinye uravneniya ellipticheskogo tipa, Nauka, M., 1964