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 { Δ u ± | ∇ u | q = b ( x ) f ( u ) , x ∈ Ω , u ( x ) = + ∞ , x ∈ ∂ Ω , where Ω is a smooth bounded domain in R N . The weight function 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 ) ∈ C 2 [ 0 , + ∞ ) is increasing on ( 0 , ∞ ) satisfying the Keller–Osserman condition, and regularly varying at infinity with index ρ > 1 .