Two nontrivial solutions of a class of elliptic equations with singular term

Abstract

We consider the existence of nontrivial solutions of the equation -Δu -λ/|x|2 u = |u|2*-2u + μ|x| α-2u + f(x)|u|γ, x ∈Ω\ -0}, u∈ H 01 (Ω); where 0 ∈ Ω is a smooth bounded domain in ℝN (N ≥ 3). By variational methods and Nehari set techniques, we show that this equation has at least two nontrivial solutions in H0 1 (Ω), under some additional hypotheses on λ > 0, μ > 0, α > 0, 0 ≤ γ < 1 and f ∈ L∞(Ω), which may be sign-changing. If f > 0 then the solutions are positive.