Ground states for fractional Choquard equations with magnetic fields and critical exponents

In this paper, we investigate the ground states for the following fractional Choquard equation with magnetic fields and critical exponents: (-Delta)(A)(s) u + V(x)u = lambda f(x, u) + [vertical bar x vertical bar(-alpha) * vertical bar u vertical bar(2 alpha,s)*(-2)u in R-N, where lambda > 0, alpha epsilon (0, 2s), N > 2s, u : R-N -> C is a complex-valued function, 2(alpha,s)* = (2N - alpha)/(N - 2s) is the fractional Hardy-Littlewood-Sobolev critical exponent, V epsilon (R-N, R) is an electric potential, V and f are asymptotically periodic in x, A epsilon (R-N, R-N) is a magnetic potential, and (-Delta)(A)(s) is a fractional magnetic Laplacian operator with s epsilon (0, 1). We prove that the equation has a ground state solution for large lambda by using the Nehari method and the concentration-compactness principle.