Existence and symmetry of positive ground states for a doubly critical Schrodinger system

Zhijie Chen, Wenming Zou

We study the following doubly critical Schrödinger system $$-Δu -\frac{\la_1}{|x|^2}u=u^{2^\ast-1}+ ν\al u^{\al-1}v^\bb, \quad x\in \RN, -Δv -\frac{\la_2}{|x|^2}v=v^{2^\ast-1} + ν\…