Existence of ground states for fractional Choquard-Kirchhoff equations withmagnetic fields and critical exponents

In this paper, we consider the following fractional Choquard-Kirchhoff equation with magnetic fields and critical exponents M([u](s,A)(2))(-Delta)(A)(s)u + V(x)u = [|x|-alpha * |u|(2)(alpha,s)*]|u|(2)(alpha,s)* -(2)u + lambda f (x, u) in R-N, where N > 2s with 0 < s < 1, lambda > 0, A = ( A1, A2,..., An) is an element of (R-N, R-N) is a magnetic potential, 2(alpha,s)* = (2N - alpha)/( N - 2s) is the fractional Hardy-Littlewood-Sobolev critical exponent with 0 < alpha < 2s, M([u](s,A)(2)) = a + b[u](s, A)(2) with a, b > 0, u. (R-N, C) is a complex valued function, V is an element of L-infinity (R-N) and f is an element of (R-N x R, R) are continuous functions, (-Delta)(A)(s) is a fractional magnetic Laplacian operator. Under some suitable assumptions, by applying the Nehari method and the concentration-compactness principle, we obtain the existence of ground state solutions.