## Differential and Integral Equations

### 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 $\varepsilon.$ 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.

#### Article information

Source
Differential Integral Equations, Volume 30, Number 3/4 (2017), 231-258.

Dates
First available in Project Euclid: 18 February 2017

Permanent link to this document
https://projecteuclid.org/euclid.die/1487386824

Mathematical Reviews number (MathSciNet)
MR3611500

Zentralblatt MATH identifier
06738549

#### Citation

Murcia, Edwin G.; Siciliano, Gaetano. Positive semiclassical states for a fractional Schrödinger-Poisson system. Differential Integral Equations 30 (2017), no. 3/4, 231--258. https://projecteuclid.org/euclid.die/1487386824