Positive semiclassical states for a fractional Schr\"odinger-Poisson system
Analysis of PDEs
2016-01-05 v1
Abstract
We consider a fractional Schr\"odinger-Poisson system in the whole space in presence of a positive potential and depending on a small positive parameter We show that, for suitably small (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.
Keywords
Cite
@article{arxiv.1601.00485,
title = {Positive semiclassical states for a fractional Schr\"odinger-Poisson system},
author = {Edwin G. Murcia and Gaetano Siciliano},
journal= {arXiv preprint arXiv:1601.00485},
year = {2016}
}