Geodesic
Existence of positive solutions for Dirichlet problems of some singular elliptic equations
Electronic Journal of Differential Equations, Tome 2003 (2003).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: When an unbounded domain is inside a slab, existence of a positive solution is proved for the Dirichlet problem of a class of semilinear elliptic equations similar to the singular Emden-Fowler equation. The proof is based on a super and sub-solution method. A super solution is constructed by Perron's method together with a family of auxiliary functions.
Classification : 35J25, 35J60, 35J65
Keywords: elliptic boundary value problems, positive solutions, singular semilinear equations, unbounded domains, Perron's method, super solutions 
@article{EJDE_2003__2003__a148,
     author = {Jin, Zhiren},
     title = {Existence of positive solutions for {Dirichlet} problems of some singular elliptic equations},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2003},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a148/}
}
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Jin, Zhiren. Existence of positive solutions for Dirichlet problems of some singular elliptic equations. Electronic Journal of Differential Equations, Tome 2003 (2003). http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a148/