Positive semiclassical states for a fractional Schrödinger-Poisson system

2016/01/04 by Murcia, Edwin G., Siciliano, Gaetano · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1601.00485

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 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.

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• Fractional Schrödinger-Poisson-Slater equations in Coulomb-Sobolev spaces

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