An exact estimate result for a class of singular equations with critical exponents

We consider the singular boundary value problem−Δu=h(x)uγ+λup−1in Ω,u=0on ∂Ω with p=2N/(N−2)p=2N/(N−2), γ∈(0,1)γ∈(0,1). It is well known that there exists λ⁎>0λ⁎>0 such that the problem has a solution for all λ∈(0,λ⁎)λ∈(0,λ⁎) and no solution for λ>λ⁎λ>λ⁎. We obtain an exact result for λ⁎(Ω,p,γ,h)λ⁎(Ω,p,γ,h).