Geodesic
Positive solutions of second order elliptic equations in unbounded domains
Sbornik. Mathematics, Tome 54 (1986) no. 1, pp. 129-134 
E. M. Landis; N. S. Nadirashvili. Positive solutions of second order elliptic equations in unbounded domains. Sbornik. Mathematics, Tome 54 (1986) no. 1, pp. 129-134. http://geodesic.mathdoc.fr/item/SM_1986_54_1_a6/
@article{SM_1986_54_1_a6,
     author = {E. M. Landis and N. S. Nadirashvili},
     title = {Positive solutions of second order elliptic equations in unbounded domains},
     journal = {Sbornik. Mathematics},
     pages = {129--134},
     year = {1986},
     volume = {54},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1986_54_1_a6/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $L$ be a second order uniformly elliptic operator defined in an unbounded domain $G$. The problem is considered of determining a solution positive in $G$ of the equation $Lu=0$ in $G$ with zero Dirichlet data on the boundary of the domain. The existence and uniqueness (to within multiplication by a positive constant) of a solution of this problem is established for some unbounded domains. Bibliography: 3 titles.

[1] Krylov N. V., Safonov M. V., “Nekotoroe svoistvo reshenii parabolicheskikh uravnenii s izmerimymi koeffitsientami”, Izv. AN SSSR. Ser. matem., 44 (1980), 161–175 | MR | Zbl

[2] Moser J., “On Harnack's theorem for elliptic differential equations”, Comm. Pure and Appl. Math., 14:3 (1961), 577–591 | DOI | MR | Zbl

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