Asymptotic Behavior of The Unique Solution to a Singular Elliptic Problem With Nonlinear Convection Term And Singular Weight
Zhijun Zhang · Advanced Nonlinear Studies · 2008
Abstract 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) > 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 > 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.