A construction of singular solutions for a semilinear elliptic equation using asymptotic analysis

The aim of this paper is to prove the existence of weak solutions to the equation Au + u p = 0 which are positive in a domain C R N , vanish at the boundary, and have prescribed isolated singularities. The exponent p is required to lie in the interval (N/(N -2),(JV + 2)/(N -2)). We also prove the existence of solutions to the equation u + u p = 0 which are positive in a domain cK n and which are singular along arbitrary smooth -dimensional submanifolds in the interior of these domains provided p lies