Existence of concentrating positive solutions u_ε for the fractional nonlinear Schrödinger-Poisson system with critical nonlinearity as ε→0 under suitable assumptions on V and g.
Positive semiclassical states for a fractional Schr\"odinger-Poisson system
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abstract
We consider a fractional Schr\"odinger-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.
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math.AP 1years
2019 1verdicts
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Concentrating phenomenon for fractional nonlinear Schr\"{o}dinger-Poisson system with critical nonlinearity
Existence of concentrating positive solutions u_ε for the fractional nonlinear Schrödinger-Poisson system with critical nonlinearity as ε→0 under suitable assumptions on V and g.