Boundary blow-up rates of large solutions for elliptic equations with convection terms

By Karamata regular variation theory, a perturbation method and constructing comparison functions, we show the exact asymptotic behavior of large solutions to the semilinear elliptic equations with convection terms{Δu±|∇u|q=b(x)f(u),x∈Ω,u(x)=+∞,x∈∂Ω, where Ω   is a smooth bounded domain in RNRN. The weight function b(x)b(x) is a non-negative continuous function in the domain, which may be vanishing on the boundary or be singular on the boundary. f(u)∈C2[0,+∞)f(u)∈C2[0,+∞) is increasing on (0,∞)(0,∞) satisfying the Keller–Osserman condition, and regularly varying at infinity with index ρ>1ρ>1.