Positive semiclassical states for a fractional Schrödinger-poisson system

Edwin G. Murcia; Gaetano Siciliano; Jean Mawhin

Positive semiclassical states for a fractional Schrödinger-poisson system

Edwin G. Murcia
, Gaetano Siciliano
, Jean Mawhin

Universidade de São Paulo

Research output: Contribution to journal › Article › peer-review

72 Scopus citations

Abstract

We consider a fractional Schrödinger-Poisson system in the whole space ℝ^N in presence of a positive potential and depending on a small positive parameter ϵ. We show that, for suitably small ϵ (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.

Original language	English
Pages (from-to)	231-258
Number of pages	28
Journal	Differential and Integral Equations
Volume	30
Issue number	3-4
State	Published - 01 Mar 2017
Externally published	Yes

Cite this

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title = "Positive semiclassical states for a fractional Schr{\"o}dinger-poisson system",

abstract = "We consider a fractional Schr{\"o}dinger-Poisson system in the whole space ℝN in presence of a positive potential and depending on a small positive parameter ϵ. We show that, for suitably small ϵ (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.",

author = "Murcia, \{Edwin G.\} and Gaetano Siciliano and Jean Mawhin",

year = "2017",

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T1 - Positive semiclassical states for a fractional Schrödinger-poisson system

AU - Murcia, Edwin G.

AU - Siciliano, Gaetano

AU - Mawhin, Jean

PY - 2017/3/1

Y1 - 2017/3/1

N2 - We consider a fractional Schrödinger-Poisson system in the whole space ℝN in presence of a positive potential and depending on a small positive parameter ϵ. We show that, for suitably small ϵ (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.

AB - We consider a fractional Schrödinger-Poisson system in the whole space ℝN in presence of a positive potential and depending on a small positive parameter ϵ. We show that, for suitably small ϵ (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.

UR - https://www.scopus.com/pages/publications/85017328054

M3 - Article

AN - SCOPUS:85017328054

SN - 0893-4983

VL - 30

SP - 231

EP - 258

JO - Differential and Integral Equations

JF - Differential and Integral Equations

IS - 3-4

ER -

Positive semiclassical states for a fractional Schrödinger-poisson system

Abstract

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