Existence of positive solutions for a critical fractional Kirchhoff equation with potential vanishing at infinity

In this paper, we consider the following fractional Kirchhoff equation with critical nonlinearitya + b ∫ R 3( − Δ ) s 2 u 2d x( − Δ ) s u + V ( x ) u = Q ( x ) f ( u ) + | u |2 s ∗ − 2 u , x ∈ R 3 ,where a , b > 0 ,( − Δ ) s is the fractional Laplace operator with s ∈ ( 3 4 , 1 ) , V vanishes at infinity and2 s ∗ = 6 3 − 2 s. Under appropriate assumptions on f , we prove the existence of positive solution by using the variational method.