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^su+V(x)u=[|x|^-α*|u|^2^*_α ,s]|u|^2^*_α ,s-2u+λ f(x,u) in ℝ^N, where N>2s with 00 , A=(A_1,A_2,… ,A_n)∈ (ℝ^N,ℝ^N) is a magnetic potential, 2^*_α ,s=(2N-α )/(N-2s) is the fractional Hardy—Littlewood—Sobolev critical exponent with 0<α <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∈ L^∞(ℝ^N) and f∈ (ℝ^N×ℝ,ℝ) are continuous functions, (-Δ )^s_A 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.