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