Existence and uniqueness of solutions for a singular semilinear elliptic system

摘要

In this paper, we study the existence and the uniqueness of solutions for the singular semilinear elliptic system: where 0 < p < 1 and 0 < q < 1. We show the existence of a solution for an approximated system by using a perturbation method which eliminates the singularity and via variational methods. The limit of the approximated solutions is a positive solution. In the case g = 0, p = q and 1/2 < p < 1, we prove the uniqueness of solution. The proofs rely on the concentration-compactness principle.