Nonlinear Choquard equations involving a critical local term

We consider a critical version of nonlinear Choquard equation {−Δu+u=(Iα∗|u|p)|u|p−2u+λ|u|2∗−2uin  RN,limx→∞u(x)=0, where Iα denotes the Riesz potential. This equation can be seen as a nonlocal perturbation of the usual critical problem in a whole space. Using some perturbation arguments, we construct a family of nontrivial solutions, which converges to a least energy solution of the limiting critical local problem as α→0.