Positive semiclassical states for a fractional Schr\"odinger-Poisson system

We consider a fractional Schr"odinger-Poisson system in the whole space ${\mathbb{R}}^N$ in presence of a positive potential and depending on a small positive parameter $\epsilon \mathrm{.}$ We show that, for suitably small $\epsilon$ (i.e. in the “semiclassical limit”) the number of positive solutions is estimated below by the Ljusternick-Schnirelmann category of the set of minima of the potential.