We consider the following fractional Schrödinger-Poisson equation with combined nonlinearities
$ \begin{equation*} \begin{cases} (-\Delta)^su+\phi u = |u|^{s^*-2}u+\mu|u|^{p-2}u \,\,\,\rm{in}\ \mathbb{R}^3,\\ -\Delta \phi = 4\pi u^2\ \rm{in}\ \mathbb{R}^3, \end{cases} \end{equation*} $
where $ s\in(\frac{3}{4},1) $, $ \mu>0 $, $ p\in(3,s^*) $ and $ s^* = \frac{6}{3-2s} $. By the perturbation approach we prove the existence of the ground state solution in fractional Coulomb-Sobolev space.
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