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

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

Tsing-San Hsu

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

Received 9 October 2009; Accepted 12 February 2010

Academic Editor: Kanishka Perera

Copyright © 2010 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 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.