Second order expansion for blowup solutions of semilinear elliptic problems

Abstract

In this paper, we mainly study the second order expansion of solutions to the elliptic problems △ u = b ( x ) f ( u ) , u > 0 , x ∈ Ω , u | ∂ Ω = ∞ , where Ω is a bounded domain with a smooth boundary in R N ( N ≥ 2 ) , b ∈ C α ( Ω ̄ ) which is positive in Ω and may be vanishing on the boundary and f is normalized regularly varying at infinity with index p > 1 . Our analysis is based on the sub-supersolution method and Karamata regular variation theory.