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

Correspondence should be addressed to Tsing-San Hsu, [email protected] Received 9 October 2009; Accepted 12 February 2010 Academic Editor: Kanishka Perera Copyright q 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. We consider the following class of quasilinear elliptic equations −hΔpu Vε x |u|p−2u |u|q−2u, u x > 0 for all x ∈ R , 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.