Ground state for fractional Schrödinger-Poisson equation in Coulomb-Sobolev space

Abstract

We consider the following fractional Schrödinger-Poisson equation with combined nonlinearitieswhere s ∈ ( 3 4 , 1), µ > 0, p ∈ (3, s * ) and s * = 6 3−2s . By the perturbation approach we prove the existence of the ground state solution in fractional Coulomb-Sobolev space.