Geodesic
Existence of positive solutions for Dirichlet problems of some singular elliptic equations
Electronic journal of differential equations, Tome 2003 (2003)
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},
     year = {2003},
     volume = {2003},
     zbl = {1109.35338},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a148/}
}
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JO  - Electronic journal of differential equations
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%A Jin,  Zhiren
%T Existence of positive solutions for Dirichlet problems of some singular elliptic equations
%J Electronic journal of differential equations
%D 2003
%V 2003
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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/