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

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.