Electron. J. Diff. Eqns., Vol. 2005(2005), No. 44, pp. 1-16.

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

Imed Bachar, Habib Mâagli, Malek Zribi

Abstract:
This paper concerns nonlinear elliptic equations in the half space $\mathbb{R}_{+}^{n}:=\{ x=(x',x_{n})\in \mathbb{R}^{n}:x_{n}$ greater than 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

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Imed Bachar
Département de Mathématiques
Faculté des Sciences de Tunis
Campus universitaire 1060 Tunis, Tunisia
e-mail: Imed.Bachar@ipeit.rnu.tn
Habib Mâagli
Département de Mathématiques
Faculté des Sciences de Tunis
Campus universitaire 1060 Tunis, Tunisia
e-mail: habib.maagli@fst.rnu.tn
Malek Zribi
Département de Mathématiques
Faculté des Sciences de Tunis
Campus universitaire, 1060 Tunis, Tunisia
email: malek.Zribi@insat.rnu.tn

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