Geodesic
On properties of solutions of a class of nonlinear second-order equations
Sbornik. Mathematics, Tome 83 (1995) no. 1, pp. 67-77 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The boundary value problem $$ Lu=f(|u|) \quad \text {in}\quad \Omega , \qquad u\big|_{\partial \Omega }=w, $$ is studied, where $\Omega$ is an arbitrary, possibly unbounded, open subset of $R^n$, $L=\sum\limits_{i,j=1}^n\dfrac \partial {\partial x_i} \biggl(a_{ij}(x)\dfrac \partial {\partial x_j}\biggr)$ is a differential operator of elliptic type with measurable coefficients, and $w$, $f$ are some functions. 
@article{SM_1995_83_1_a2,
     author = {V. A. Kondrat'ev and A. A. Kon'kov},
     title = {On properties of solutions of a~class of nonlinear second-order equations},
     journal = {Sbornik. Mathematics},
     pages = {67--77},
     year = {1995},
     volume = {83},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1995_83_1_a2/}
}
TY  - JOUR
AU  - V. A. Kondrat'ev
AU  - A. A. Kon'kov
TI  - On properties of solutions of a class of nonlinear second-order equations
JO  - Sbornik. Mathematics
PY  - 1995
SP  - 67
EP  - 77
VL  - 83
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SM_1995_83_1_a2/
LA  - en
ID  - SM_1995_83_1_a2
ER  - 
%0 Journal Article
%A V. A. Kondrat'ev
%A A. A. Kon'kov
%T On properties of solutions of a class of nonlinear second-order equations
%J Sbornik. Mathematics
%D 1995
%P 67-77
%V 83
%N 1
%U http://geodesic.mathdoc.fr/item/SM_1995_83_1_a2/
%G en
%F SM_1995_83_1_a2
V. A. Kondrat'ev; A. A. Kon'kov. On properties of solutions of a class of nonlinear second-order equations. Sbornik. Mathematics, Tome 83 (1995) no. 1, pp. 67-77. http://geodesic.mathdoc.fr/item/SM_1995_83_1_a2/

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

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

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

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

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

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

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

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

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

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

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

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

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