A uniqueness result for some singular semilinear elliptic equations

Given Ω a bounded open subset of ℝN, we consider non-negative solutions to the singular semilinear elliptic equation − Δu = f uβ in Hloc1(Ω), under zero Dirichlet boundary conditions. For β > 0 and f ∈ L1(Ω), we prove that the solution is unique.