Asymptotic behavior of large solution to elliptic equation of Bieberbach–Rademacher type with convection terms

摘要

We analyze the asymptotic behavior of solutions to nonlinear elliptic equation Δu±|∇u|q=b(x)f(u) in Ω, subject to the singular boundary condition u(x)=∞ as dist(x,∂Ω)→0, where Ω is a smooth bounded domain in RN, f∘L∈RVρ(ρ>0) for some L∈C2[A,∞), limu→∞L(u)=∞ and L′∈NRV-1. Our approach employs Karamata regular variation theory combined with the method of lower and supper solution.