Positive Semiclassical States for a Fractional Schrodinger-poisson System

We consider a fractional Schrödinger-Poisson system in the whole space R^N in presence of a positive potential and depending on a small positive parameter ε. We show that, for suitably small ε (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.