Nonlinear Choquard equations involving a critical local term

We consider a critical version of nonlinear Choquard equation {-Delta u + u = (I-alpha * vertical bar u vertical bar(p-2)u + lambda vertical bar u vertical bar(2)*(-2)u in R-N, [GRAPHICS] u(x) = 0, where I-alpha 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 alpha -> 0. (C) 2016 Elsevier Ltd. All rights reserved.