Boundary behaviour of the unique solution to a singular Dirichlet problem with a convection term

摘要

By Karamata regular variation theory and constructing comparison functions, we derive that the boundary behaviour of the unique solution to a singular Dirichlet problem - Δ u = b (x) g (u) + λ | ? u |~q, u > 0, x ∈ Ω, u |_(? Ω) = 0, which is independent of λ | ? u_λ |~q, where Ω is a bounded domain with smooth boundary in R~N, λ ∈ R, q ∈ (0, 2], lim_(s → 0+) g (s) = + ∞, and b is non-negative on Ω, which may be vanishing on the boundary.