The uniqueness of blow-up solution for radially symmetric semilinear elliptic equation

In this paper we establish a blow up rate of the large positive solutions of the singular boundary value problem -Δu=λu-b(x)up,u|∂Ω=+∞ with a ball domain and radially function b(x). All previous results in the literature assumed the decay rate of b(x) to be approximated by a distance function near the boundary ∂Ω. Obtaining the accurate blow up rate of solutions for general b(x) requires more subtle mathematical analysis of the problem.