Geodesic
Positive solutions of singular elliptic equations outside the unit disk
Electronic journal of differential equations, Tome 2001 (2001)
We study the existence and the asymptotic behaviour of positive solutions for the nonlinear singular elliptic equation $\Delta u +\varphi(.,u)=0$ in the outside of the unit disk in $\mathbb{R}^2$, with homogeneous Dirichlet boundary condition. The aim is to prove some existence results for the above equation in a general setting by using a potential theory approach.
Classification : 34B16, 34B27, 35J65
Keywords: singular elliptic equation, Green function, Schauder fixed point theorem, maximum principle, superharmonic function 
@article{EJDE_2001__2001__a57,
     author = {Zeddini,  Noureddine},
     title = {Positive solutions of singular elliptic equations outside the unit disk},
     journal = {Electronic journal of differential equations},
     year = {2001},
     volume = {2001},
     zbl = {0985.34015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a57/}
}
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%J Electronic journal of differential equations
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Zeddini,  Noureddine. Positive solutions of singular elliptic equations outside the unit disk. Electronic journal of differential equations, Tome 2001 (2001). http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a57/