Electron. J. Diff. Eqns., Vol. 2001(2001), No. 53, pp. 1-20.

Positive solutions of singular elliptic equations outside the unit disk

Noureddine Zeddini

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.

Submitted February 13, 2001. Published July 24, 2001.
Math Subject Classifications: 34B16, 34B27, 35J65.
Key Words: Singular elliptic equation, Green function, Schauder fixed point theorem, maximum principle, superharmonic function.

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Noureddine Zeddini
Departement de Mathematiques
Faculte des Sciences de Tunis
Campus Universitaire, 1060 Tunis, Tunisia
e-mail: Noureddine.Zeddini@ipein.rnu.tn

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