Abstract and Applied Analysis 
Volume 2006 (2006), Article ID 24307, 13 pages
doi:10.1155/AAA/2006/24307

Existence of positive solutions for some nonlinear elliptic problems in unbounded domains of ℝn

Noureddine Zeddini

 Département de Mathématiques, Faculté des Sciences de Tunis, Campus Universitaire, Tunis 2092, Tunisia
Received 26 May 2005; Accepted 1 August 2005

Abstract

This paper deals with a class of nonlinear elliptic equations in an unbounded domain D of ℝn, n≥3, with a nonempty compact boundary, where the nonlinear term satisfies some appropriate conditions related to a certain Kato class K∞(D). Our purpose is to give some existence results and asymptotic behaviour for positive solutions by using the Green function approach and the Schauder fixed point theorem.