The blow-up rate and uniqueness of large solution for a porous media logistic equation

In this paper we ascertain the exact blow-up rate of the large solutions of a class of sublinear elliptic problems of a logistic type related to the porous media equation, from which we can obtain the uniqueness of the solution. The weight function in front of the nonlinearity vanishes on the boundary of the underlying domain with a general decay rate which can be approximated by a distance function.