Existence of positive solutions for a class of critical fractional Schrödinger-Poisson system with potential vanishing at infinity

Abstract In this paper, we study the following fractional Schrodinger-Poisson system ( − Δ ) s u + V ( x ) u + ϕ u = K ( x ) f ( u ) + | u | 2 s ∗ − 2 u , in R 3 , ( − Δ ) t ϕ = u 2 , in R 3 , where s ∈ ( 3 4 , 1 ) , t ∈ ( 0 , 1 ) are fixed constants, ( − Δ ) s is the fractional Laplace operator, 2 s ∗ = 6 3 − 2 s , V and K are positive functions and f is continuous, superlinear at infinity with quasicritical growth. We show that the above equation has a positive solution via the variational method.