Symmetry results for decay solutions of elliptic systems in the whole space

In this paper, by using the Alexandrov–Serrin method of moving planes combined with maximum principles, we prove that the decaying positive solutions of a semi-linear elliptic system in the whole space are radially symmetric about some point. The system under our consideration includes the important physical interesting case, the stationary Schrödinger system for Bose–Einstein condensate.