Existence of ground states for fractional Choquard–Kirchhoff equations with magnetic 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 ) ( - Δ ) A s u + V ( x ) u = [ | x | - α ∗ | u | 2 α , s ∗ ] | u | 2 α , s ∗ - 2 u + λ f ( x , u ) in R N , where N > 2 s with 0 < s < 1 , λ > 0 , A = ( A 1 , A 2 , … , A n ) ∈ ( R N , R N ) is a magnetic potential, 2 α , s ∗ = ( 2 N - α ) / ( N - 2 s ) is the fractional Hardy—Littlewood—Sobolev critical exponent with 0 < α < 2 s , 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 ∈ L ∞ ( R N ) and f ∈ ( R N × R , R ) are continuous functions, ( - Δ ) 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.