Electronic Journal of Differential Equations,
Vol. 2001(2001), No. 53, pp. 1-20.

Title: Positive solutions of singular elliptic equations outside the unit disk
   
Author: Noureddine Zeddini (Faculte des Sciences de Tunis, Tunisia)

Abstract:  
 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.