Multiplicity result for a class of elliptic equations with singular term

We consider the existence of nontrivial solutions of the equation −Δu−λ|x|2u=|u|2∗−2u+μ|x|α−2u+f(x)|u|γ,x∈Ω∖{0},u∈H01(Ω), where 0∈Ω0∈Ω is a smooth bounded domain in RNRN (N≥3N≥3). By variational methods and Nehari set techniques, we show that this problem, under some additional hypotheses on λ>0λ>0, μ>0μ>0, α>0α>0, 0≤γ<10≤γ<1 and f∈L∞(Ω)f∈L∞(Ω), has four nontrivial solutions in H01(Ω), and that least one of them is sign-changing.