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By Karamata regular variation theory, we first derived the exact asymptotic behavior of the local solution to the problem -φʹʹ(s) = g(φ(s)), φ(s) &gt; 0, s ∈ (0, a) and φ(0) = 0. Then, by a perturbation method and constructing comparison functions, we derived the exact asymptotic behavior of the unique classical solution near the boundary to a singular Dirichlet problem -Δu = b(x)g(u) + λ|▽u| q , u &gt; 0, x ∈ Ω, u| aΩ  = 0, where Ω is a bounded domain with smooth boundary, λ ∈ ℝ, q ∈ [0, 2]; g ∈ C 1 ((0, ∞), (0, ∞)), is decreasing in (0, ∞) with lim s→0  + g(s) = +∞; the weight b is positive in Ω and singular on the boundary.

Asymptotic Behavior of The Unique Solution to a Singular Elliptic Problem With Nonlinear Convection Term And Singular Weight