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

Abstract We consider the singular boundary value problem − Δ u = h ( x ) u γ + λ u p − 1 in Ω , u = 0 on ∂ Ω with p = 2 N / ( 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 ) .