English

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 RN\mathbb R^{N} in presence of a positive potential and depending on a small positive parameter ε.\varepsilon. We show that, for suitably small ε\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.

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}
}