半线性椭圆型问题大解的二阶估计

In this paper, we investigate the second term asymptotic behavior of boundary blowup solutions to the problem Δu=b(x)f(u),x∈Ω, subject tothe singular boundary condition u(x)=∞ in smooth bounded domains Ω∈R N(N≥3). Where b(x) is a non-negative weight function, which may be vanishing on the boundary or be singular on the boundary. The absorption term f is regularly varying at infinity with index ρ>1 andthe mapping f(u)/u is increasing on (0,+∞). Our analysis relies on the Karamata regular variation therory.