论文标题
$ \ mathbb {r}^2 $中的Schrödinger-Poisson系统的浓度现象
Concentration phenomena for the Schrödinger-Poisson system in $\mathbb{R}^2$
论文作者
论文摘要
我们对平面Schrödinger-Poisson系统进行半古典分析 \ [ \ case { - \ \ varepsilon^{2}Δψ+v（x）ψ= e（x）ψ\ quad \ text {in $ \ m athbb {r}^2 $}，\ cr -ΔE= |ψ|^{2} \ Quad \ text {in $ \ m athbb {r}^2 $}，\ cr } \ tag {$ sp_ \ varepsilon $} \] 其中$ \ varepsilon $是与普朗克常数相对应的正参数，而$ v $是有界的外部电位。我们检测到系统$（sp_ \ varepsilon）$的解决方案对$（u_ \ varepsilon，e_ \ varepsilon）$作为〜$ \ ge \ ge \ rightarrow 0 $。
We perform a semiclassical analysis for the planar Schrödinger-Poisson system \[ \cases{ -\varepsilon^{2} Δψ+V(x)ψ= E(x) ψ\quad \text{in $\mathbb{R}^2$},\cr -ΔE= |ψ|^{2} \quad \text{in $\mathbb{R}^2$}, \cr } \tag{$SP_\varepsilon$} \] where $\varepsilon$ is a positive parameter corresponding to the Planck constant and $V$ is a bounded external potential. We detect solution pairs $(u_\varepsilon, E_\varepsilon)$ of the system $(SP_\varepsilon)$ as~$\ge \rightarrow 0$.
