Asymptotic behavior of positive solutions of a singular nonlinear Dirichlet problem

Abstract

Let Ω be a C 1 , 1 -bounded domain in R n 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 Δ u + a ( x ) u − σ = 0 in Ω, u | ∂ Ω = 0 , where σ ⩾ 0 , a is a nonnegative function in C loc α ( Ω ) , 0 < α < 1 and there exists c > 0 such that 1 c ⩽ a ( x ) ( δ ( x ) ) λ ∏ k = 1 m ( Log k ( ω δ ( x ) ) ) μ k ⩽ c . Here λ ⩽ 2 , μ k ∈ R , ω is a positive constant and δ ( x ) = dist ( x , ∂ Ω ) .