Multiplicity of positive solutions for semilinear elliptic problems in unbounded domains

In this paper, we study the effect of domain shape on the multiplicity of positive solutions for the semilinear elliptic equations. We prove a Palais–Smale condition in unbounded domains and assert that the semilinear elliptic equation in unbounded domains has multiple positive solutions. © 2006 Elsevier Inc. All rights reserved