Multiple positive solutions for an unbounded Dirichlet boundary problem involving sign-changing weight

Abstract

We study the multiplicity of positive solutions for the following semilinear elliptic equation:where 1 < q < 2 < p < 2* (2* = 2N/(N − 2) if N ≥ 3, 2* = ∞ if N = 2), the parameters λ, μ ≥ 0, is an infinite strip in ℝN and Θ is a bounded domain in ℝN−1 We assume that fλ(x) = λf+(x) + f−(x) and gμ(x) = a(x) + μb(x), where the functions f±, a and b satisfy suitable conditions.