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
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.