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
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.