Boundary Value Problems
Volume 2009 (2009), Article ID 687385, 20 pages
doi:10.1155/2009/687385
Research Article

Multiplicity of Positive and Nodal Solutions for Nonhomogeneous Elliptic Problems in Unbounded Cylinder Domains

Tsing-San Hsu

Center for General Education, Chang Gung University, Kwei-San, Tao-Yuan 333, Taiwan

Received 13 March 2009; Accepted 7 May 2009

Academic Editor: Zhitao Zhang

Copyright © 2009 Tsing-San Hsu. 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

We show that if a(x) and f(x) satisfy some suitable conditions, then the Dirichlet problem −Δu+u=a(x)|u|p−2u+f(x) in Ω has a solution that changes sign in Ω, in addition to two positive solutions where Ω is an unbounded cylinder domain in ℝN.