Electronic Journal of Differential Equations,
Vol. 2002(2002), No. 41, pp. 1-24.

Title: Positive solutions of nonlinear elliptic equations in a half
       space in $R^2$
   
Authors: Imed Bachar (Faculte des Sciences de Tunis, Tunisia)
 Habib Maagli (Faculte des Sciences de Tunis, Tunisia)
 Lamia Maatoug (Faculte des Sciences de Tunis, Tunisia)

Abstract: 
  We study the existence and the asymptotic behaviour of positive
  solutions of the nonlinear equation 
  $\Delta u+f(.,u)=0$, 
  in   the domain 
  $D=\{(x_1,x_2)\in \mathbb{R}^2:x_2>0\}$, 
  with $u=0$ on  the boundary.   
  The aim is to prove some existence results
  for the above equation in a general setting by using a
  fixed-point argument.

Submitted December 14, 2001. Published May 16, 2002.
Math Subject Classifications: 31A25, 31A35, 34B15, 34B27, 35J65. 
Key Words: Singular elliptic equation; superharmonic function;
    Green function; Schauder fixed point theorem; maximun principle.