Positive semiclassical states for a fractional Schrödinger-Poisson system

Abstract

We consider a fractional Schrödinger-Poisson system in the whole space ${\mathbb{R}}^N$ in presence of a positive potential and depending on a small positive parameter $\epsilon .$ 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.

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