Multiple existence of solutions for a nonhomogeneous elliptic problem on RN

Let N 3, 2∗ = 2N N−2 and p ∈ (2, 2∗). Our purpose in this paper is to consider multiple existence of solutions of problem − u +u = |u|p−2u+ f, u ∈ H1 RN , where f ∈ L2(RN), f 0 and f ≡ 0. © 2007 Elsevier Inc. All rights reserved.