On qualitative properties of solutions of a nonlinear equation of second order
Sbornik. Mathematics, Tome 63 (1989) no. 2, pp. 337-350 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A number of theorems are obtained on the behavior of solutions of second-order elliptic equations containing nonlinearities. Among them are a theorem on the uniqueness of the solutions of the exterior Dirichlet problem, a theorem on a removable singularity, and a theorem on the absence of entire solutions. Bibliography: 15 titles.
@article{SM_1989_63_2_a4,
     author = {V. A. Kondrat'ev and E. M. Landis},
     title = {On qualitative properties of solutions of a~nonlinear equation of second order},
     journal = {Sbornik. Mathematics},
     pages = {337--350},
     year = {1989},
     volume = {63},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1989_63_2_a4/}
}
TY  - JOUR
AU  - V. A. Kondrat'ev
AU  - E. M. Landis
TI  - On qualitative properties of solutions of a nonlinear equation of second order
JO  - Sbornik. Mathematics
PY  - 1989
SP  - 337
EP  - 350
VL  - 63
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_1989_63_2_a4/
LA  - en
ID  - SM_1989_63_2_a4
ER  - 
%0 Journal Article
%A V. A. Kondrat'ev
%A E. M. Landis
%T On qualitative properties of solutions of a nonlinear equation of second order
%J Sbornik. Mathematics
%D 1989
%P 337-350
%V 63
%N 2
%U http://geodesic.mathdoc.fr/item/SM_1989_63_2_a4/
%G en
%F SM_1989_63_2_a4
V. A. Kondrat'ev; E. M. Landis. On qualitative properties of solutions of a nonlinear equation of second order. Sbornik. Mathematics, Tome 63 (1989) no. 2, pp. 337-350. http://geodesic.mathdoc.fr/item/SM_1989_63_2_a4/

[1] Veron L., “Singular solutions of some nonlinear elliptic equations”, Nonlinear Analysis Theory, Methods and Appl., 5:3 (1981), 225–242 | DOI | MR | Zbl

[2] Veron L., “Solutions singuliere d'equations elliptiques semilineaires”, C. R. Acad. Sci. Ser. A, 288 (1979), 867–869 | MR | Zbl

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

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

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

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

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

[8] Levine H. A., Payne L. E., “On the nonexistence of entire solutions to nonlinear second order elliptic equations”, SIAM. J. Math. Anal., 7:3 (1976), 337 | DOI | MR | Zbl

[9] Stampacchia G., “Le probleme de Dirichlet pour les equations elliptique second ordre a coefficients discontinus”, Ann. Inst. Fourier, 15:1 (1965), 189–257 | MR | Zbl

[10] Ladyzhenskaya O. A., Uraltseva I. N., Lineinye i kvazilineinye uravneniya ellipticheskogo tipa, Nauka, M., 1964 | MR

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

[12] Gerver M. L., Landis E. M., “Odno obobschenie teoremy o srednem dlya funktsii mnogikh peremennykh”, DAN SSSR, 146:4 (1962), 761–764 | MR | Zbl

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

[14] Littman W., Stampacchia G., Weinberger B., “Regular points for elliptic equations with discontinuous coefficients”, Ann. Scuola Norm. Super. Pisa. Ser. 3, 17:1–2 (1963), 43–77 | MR | Zbl

[15] Matiichuk M. I., Edelman S. D., “O fundamentalnykh resheniyakh ellipticheskikh sistem”, Ukr. matem. zhurn., 18:2 (1966), 22–41 | MR