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.