Asymptotic behavior of positive solutions of a singular nonlinear Dirichlet problem

Let Ω be a C1,1-bounded domain in Rn for n⩾2. In this paper, we are concerned with the asymptotic behavior of the unique positive classical solution to the singular boundary-value problem Δu+a(x)u−σ=0 in Ω, u|∂Ω=0, where σ⩾0, a is a nonnegative function in , 0<α<1 and there exists c>0 such that . Here λ⩽2, μk∈R, ω is a positive constant and δ(x)=dist(x,∂Ω).