Electronic Journal of Differential Equations,
Vol. 2005(2005), No. 44, pp. 1-16.

Title: Existence of positive solutions to nonlinear 
       elliptic problem in the half space

Authors: Imed Bachar  (Faculte des Sciences de Tunis, Tunisia)
         Habib Maagli (Faculte des Sciences de Tunis, Tunisia)
	 Malek Zribi  (Faculte des Sciences de Tunis, Tunisia)

Abstract: 
 This paper concerns nonlinear elliptic equations in the
 half space  $\mathbb{R}_{+}^{n}:=\{ x=(x',x_{n})\in
 \mathbb{R}^{n}:x_{n}>0\} $, $n\geq 2$, with a nonlinear term
 satisfying some conditions related to a certain Kato
 class of functions. We prove some existence results and
 asymptotic behaviour for positive solutions using a potential
 theory approach.
 
Submitted December 20, 2004. Published April 14, 2005.
Math Subject Classifications: 34B27, 34J65.
Key Words: Green function; elliptic equation; positive solution