A Class With The Convection Term Only The Asymptotic Behavior Of Singular Nonlinear Elliptic Equation Dirichlet Problem,

By the Karamata regular variation theory, we show the exact asymptotic behaviorof the solution near 0 to a second order nonlinear ordinary differential problemThen by a perturbation method and constructing comparison functions, we studythe exact asymptotic behavior of the unique solution near theboundary to a singular Dirichlet problemwe see that the asymptotic behavior is independent on . Here,Ωis a boundeddomain with smooth boundary.λ∈R, q∈[0, 2]; g∈C¹((0,∞), (0,∞)), is non-increasing in (0,∞), and there existsγ> 1 such that g'∈RV Z_-1-γ; forsomeα∈(0, 1), is non-negative onΩand .