Second order expansion for blowup solutions of semilinear elliptic problems

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 ΩΩ is a bounded domain with a smooth boundary in RN(N≥2)RN(N≥2), b∈Cα(Ω̄) which is positive in ΩΩ and may be vanishing on the boundary and ff is normalized regularly varying at infinity with index p>1p>1. Our analysis is based on the sub-supersolution method and Karamata regular variation theory.