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

In this paper, we study the following concave–convex elliptic problems: [Formula: see text] where N ≥ 3, 1 < q < 2 < p < 2* = 2N/(N - 2), λ > 0 and μ < 0 are two parameters. By using several variational methods and a perturbation argument, we obtain three positive solutions to this problem under the predefined conditions of fλ(x) and gμ(x), which simultaneously extends the result of [T. Hsu, Multiple positive solutions for a class of concave–convex semilinear elliptic equations in unbounded domains with sign-changing weights, Bound. Value Probl. 2010 (2010), Article ID 856932, 18pp.; T. Wu, Multiple positive solutions for a class of concave–convex elliptic problems in ℝN involving sign-changing weight, J. Funct. Anal. 258 (2010) 99–131]. We also study the concentration behavior of these three solutions both for λ → 0 and μ → -∞.