Boundary Value Problems
Volume 2010 (2010), Article ID 579387, 13 pages
doi:10.1155/2010/579387

Existence and Multiplicity of Positive Solutions to a Class of Quasilinear Elliptic Equations in ℝN

Abstract

We consider the following class of quasilinear elliptic equations -hpΔpu+Vε(x)|u|p-2u=|u|q-2u, u(x)>0 for all x∈RN, where h>0, Δpu= div(|∇u|p-2∇u), 2≤p<N, p<q<p*=Np/(N-p). We allow the potential Vε to be unbounded below and prove the existence and multiplicity for positive solutions.