Multiple positive solutions for a class of concave–convex elliptic problems in RN involving sign-changing weight

In this paper, we study the multiplicity of positive solutions for the following concave–convex elliptic equation: ⎧⎨⎩ − u +u = fλ(x)uq−1 +gμ(x)up−1 in RN, u 0 in RN, u ∈ H1 RN , where 1 < q <2 < p <2∗ (2∗ = 2N N−2 if N 3, 2∗ =∞ if N = 1, 2) and the parameters λ,μ 0. We assume that fλ(x) = λf+(x)+f−(x) is sign-changing and gμ(x) = a(x)+μb(x), where the functions f±, a and b satisfy suitable conditions. © 2009 Elsevier Inc. All rights reserved.