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: {-Delta u + u = f(lambda)(x)u(q-1) + g(mu)(x)u(p-1) in R-N, u > 0 in R-N, u is an element of H-1(R-N), where N >= 3, 1 < q < 2 < p < 2* = 2N/(N-2), lambda > 0 and mu < 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 f(lambda)(x) and g(mu)(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 R-N involving sign-changing weight, J. Funct. Anal. 258 (2010) 99-131]. We also study the concentration behavior of these three solutions both for lambda -> 0 and mu -> -infinity.