Elliptic systems involving multiple critical nonlinearities and symmetric multi-polar potentials

In this paper, a system of elliptic equations is investigated, which involves multiple critical Sobolev exponents and symmetric multi-polar potentials. By variational methods and analytic techniques, the relevant best constants are studied and the existence of $left( {mathbb{Z}_k times mathbb{S}mathbb{O}left( {N - 2} right)} right)^2$ -invariant solutions to the system is established.