Multiple Positive Solutions for a Class of Concave-Convex Semilinear Elliptic Equations in Unbounded Domains with Sign-Changing Weights

Correspondence should be addressed to Tsing-San Hsu, [email protected] Received 8 September 2010; Accepted 18 October 2010 Academic Editor: Julio Rossi 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 study the existence and multiplicity of positive solutions for the following Dirichlet equations: −Δu u λa x |u|q−2u b x |u|p−2u in Ω, u 0 on ∂Ω, where λ > 0, 1 < q < 2 < p < 2∗ 2∗ 2N/ N − 2 if N ≥ 3; 2∗ ∞ if N 1, 2 , Ω is a smooth unbounded domain in N , a x , b x satisfy suitable conditions, and a x maybe change sign in Ω.