Asymptotic behaviour of the solution for the singular Lane-Emden-Fowler equation with nonlinear convection terms

Abstract

We show the exact asymptotic behaviour near the boundary for the classical solution to the Dirichler problem -Δu = k(x)g(u) + λ|∇u|q, u > 0, x ∈ Ω, u|∂Ω = 0, where Ω is a bounded domain with smooth boundary in ℝN. We use the Karamata regular varying theory, a perturbed argument, and constructing comparison functions.