Existence of Ground State Solutions for Fractional Schrödinger–Poisson Systems with Doubly Critical Growth

This paper considers a class of fractional Schrödinger–Poisson type systems with doubly critical growth ( - Δ ) s u + V ( x ) u - ϕ | u | 2 s ∗ - 3 u = K ( x ) | u | 2 s ∗ - 2 u , in R 3 , ( - Δ ) s ϕ = | u | 2 s ∗ - 1 , in R 3 , where s ∈ ( 3 / 4 , 1 ) , 2 s ∗ = 6 3 - 2 s , V ∈ L 3 2 s ( R 3 ) , K ∈ L ∞ ( R 3 ) . By applying the concentration-compactness principle and variational method, the existence of ground state solutions to the systems is derived.