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

We consider the singular boundary value problem − u = h(x) uγ +λup−1 in Ω, u =0 on∂Ω with p = 2N/(N − 2), γ ∈ (0, 1). It is well known that there exists λ ∗ > 0 such that the problem has a solution for all λ ∈ (0,λ ∗ ) and no solution for λ>λ ∗. We obtain an exact result for λ ∗ (Ω,p,γ,h). © 2010 Elsevier Inc. All rights reserved.