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arxiv: 1601.00485 · v1 · pith:A4MREOLZnew · submitted 2016-01-04 · 🧮 math.AP

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

Edwin G. Murcia , Gaetano Siciliano This is my paper
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keywords positivefractionalodinger-poissonpotentialschrsemiclassicalsmallsystem
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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 $\varepsilon.$ We show that, for suitably small $\varepsilon$ (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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