Ground state solutions for fractional Choquard equations involving upper critical exponent

Abstract In this article, we study the following fractional Choquard equation involving upper critical exponent ( − Δ ) s u + V ( x ) u = λ f ( x , u ) + [ | x | − μ ∗ | u | 2 μ , s ∗ ] | u | 2 μ , s ∗ − 2 u , x ∈ R N , where λ > 0 , 0 s 1 , ( − Δ ) s denotes the fractional Laplacian of order s , N > 2 s , 0 μ 2 s and 2 μ , s ∗ = 2 N − μ N − 2 s . When V and f are asymptotically periodic in x , we prove that the equation has a ground state solution for large λ by Nehari method.