Abstract:

This paper deals with the uniqueness of positive solutions of the Neumann problem for an elliptic system. With the help of transformation technique and maximal principle, we proved two inequalities of solutions under a definite condition, and then obtained the uniqueness of positive solution by taking the limit for them, which also shows that under more weak conditions, the problem has no any positive nonconstant solution.

Key words: elliptic system, positive solution, uniqueness