Ground states of coupled critical Choquard equations with weighted potentials

In this paper, we are concerned with the following coupled Choquard type system with weighted potentials [formula] where N ≥ 3, μ1, μ2, β > 0 and V1(x), V2(x) are nonnegative functions. Via the variational approach, one positive ground state solution of this system is obtained under some certain assumptions on V1(x), V2(x) and Q(x). Moreover, by using Hardy’s inequality and one Pohozǎev identity, a non-existence result of non-trivial solutions is also considered