Differential and Integral Equations

Positive semiclassical states for a fractional Schrödinger-Poisson system

Edwin G. Murcia and Gaetano Siciliano

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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

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

First available in Project Euclid: 18 February 2017

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35A15: Variational methods 35S05: Pseudodifferential operators 74G35: Multiplicity of solutions


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

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