A boundary blow-up for sub-linear elliptic problems with a nonlinear gradient term

Abstract

By a perturbation method and constructing comparison functions, we show the exact asymptotic behaviour of solutions to the semilinear elliptic problem Δu - |∇u|q = b(x)g(u), u > 0 in Ω, u|∂Ω = +∞, where Ω is a bounded domain in ℝN with smooth boundary, q ∈ (1, 2], g ∈ C[0, ∞) ∩ C1 (0, ∞), g(0) = 0, g is increasing on [0, ∞), and b is non-negative non-trivial in Ω, which may be singular or vanishing on the boundary.