Singular Dirichlet Problem With A Convection Term Only The Asymptotic Behavior Of The Classical Solution

We derive the boundary behaviour of the unique solution to a singular DirichletproblemwhereΩis a bounded domain with smooth boundary in R^N(N≥1),λ∈R, q∈(0, 2];g satis?es(g1) g∈C¹((0,∞), (0,∞)), g′(s) < 0 for all s > 0, (g2)b satis?es(b1) for someα∈(0, 1), is positive in ?;(b2) there exist some function k∈Λwith Ck > 0 and a positive constant b0 suchthatWhereΛdenote the set of all positive function whichsatisfyBy the properties of the local classic solution to problema perturbation method and constructing comparison functions, we showTheorem. Letλ∈R, q∈(0, 2], g satisfy (g1), (g2), b satisfy (b₁), (b₂). If k∈Λwith C_k > 0, then the unique solution u_λof problem (P) satis?eswhere...