Multiple positive solutions for a class of concave-convex semilinear elliptic equations in unbounded domains with sign-changing weights

Abstract

We study the existence and multiplicity of positive solutions for the following Dirichlet equations: - Δ u + u = λ a (x) |u| q-2 u + b (x) |u|q-2 u in ω, u = 0 on , ∂Ω, where λ > 0, 1 < q < 2 < p < 2 * (2 * = 2 N / (N - 2) if N ≥ 3; 2* = ∞ if N = 1, 2), Ω is a smooth unbounded domain in N, a (x), and b (x) satisfy suitable conditions, and a (x) maybe change sign in Ω . Copyright © 2010 Tsing-San Hsu.