Concentration phenomena for the Schrödinger-Poisson system in \begin{document}$ \mathbb{R}^2 $\end{document},Discrete and Continuous Dynamical Systems-Series S

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Concentration phenomena for the Schrödinger-Poisson system in \begin{document}$ \mathbb{R}^2 $\end{document}
Discrete and Continuous Dynamical Systems-Series S ( IF 1.3 ) Pub Date : 2020-11-16 , DOI: 10.3934/dcdss.2020447
Denis Bonheure , Silvia Cingolani , Simone Secchi

We perform a semiclassical analysis for the planar Schrödinger-Poisson system

$ \begin{gather} \begin{cases} -\varepsilon^{2} \Delta\psi+V(x)\psi = E(x) \psi \quad \text{in $ \mathbb{R}^2$}, \\ -\Delta E = |\psi|^{2} \quad \text{in $ \mathbb{R}^2$}, \end{cases} \end{gather}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (S{P_\varepsilon }) $

中文翻译：

Schrödinger-Poisson系统中的集中现象 \ begin {document} $ \ mathbb {R} ^ 2 $ \ end {document}

我们对平面Schrödinger-Poisson系统进行半经典分析

$ \ begin {gather} \ begin {cases--varepsilon ^ {2} \ Delta \ psi + V（x）\ psi = E（x）\ psi \ quad \ text {in $ \ mathbb {R} ^ 2 $}，\\-\ Delta E = | \ psi | ^ {2} \ quad \ text {in $ \ mathbb {R} ^ 2 $}，\ end {cases} \ end {gather} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \（S {P_ \ varepsilon}）$

更新日期：2020-11-16

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