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Abstract and Applied Analysis
Volume 2006, Article ID 24307, 13 pages
http://dx.doi.org/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

Copyright © 2006 Noureddine Zeddini. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.