The exact boundary behavior of the unique solution to a singular Dirichlet problem with a nonlinear convection term

摘要

In this paper we analyze the exact boundary behavior of the unique solution to the singular nonlinear Dirichlet problem -△u = b(x)g(u) + λ|?u|~q, u > 0, x ∈ Ω, u|_(?Ω) = 0, where Ω is a bounded domain with smooth boundary in ?~N, q ∈ (0, 2], λ ≥ 0, g ∈ C~1((0,∞), (0,∞)), lim_(s→0)+ g(s) = ∞, g is decreasing on (0,∞), and b ∈ C_(loc)~α (Ω), is positive in Ω, may be vanishing or singular on the boundary. We reveal that the nonlinear convection term λ|?u|~q does not affect the first expansion of the unique solution near the boundary to the problem.