Normalized ground states for the fractional Schrödinger–Poisson system with critical nonlinearities

In this paper we study the existence and properties of ground states for the fractional Schrödinger–Poisson system with combined power nonlinearities {[ (-Δ )^su-ϕ |u|^2^*_s-3u=λ u+μ |u|^q-2u+|u|^2^*_s-2u, x ∈ℝ^3,; (-Δ )^sϕ =|u|^2^*_s-1, x ∈ℝ^3, ]. having prescribed mass ∫ _ℝ^3|u|^2dx=a^2 and doubly critical growth, where s∈ (0,1) , μ >0 is a parameter, 2更多