Existence of ground state solutions for the nonlinear fractional Schrödinger–Poisson system with critical Sobolev exponent

Abstract

In this paper, we study the existence of ground state solutions for the nonlinear fractional Schrödinger–Poisson system with critical Sobolev exponent{(−Δ)su+V(x)u+ϕu=μ|u|q−1u+|u|2s⁎−2u,in R3,(−Δ)tϕ=u2,in R3, where μ∈R+ is a parameter, 1<q<2s⁎−1=3+2s3−2s, s,t∈(0,1) and 2s+2t>3. Under certain assumptions on V(x), using the method of Pohozaev–Nehari manifold and the arguments of Brezis–Nirenberg, the monotonic trick and global compactness Lemma, we prove the existence of a nontrivial ground state solution.