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.