Local estimate on singular solution to scalar curvature equation

In this paper, we study the local behavior of a positive singular solution u near its singular points of the following equation: Δu(x)+d(x,Z)2Nun+2n−2=0inΩ⧹Z,u(x)>0andu∈C2inΩ⧹Z, where N is a positive integer, Ω is a bounded open domain in Rn, Z is a finite set of points, and d(x,Z) denotes the distance between x and Z.