scholarly journals Gravitational atoms: General framework for the construction of multistate axially symmetric solutions of the Schrödinger-Poisson system

2020 ◽  
Vol 101 (8) ◽  
Author(s):  
F. S. Guzmán ◽  
L. Arturo Ureña-López
Keyword(s):  
General Framework ◽  
Poisson System ◽  
Axially Symmetric

Axially symmetric solutions of the Schrödinger–Poisson system with zero mass potential in R2

2020 ◽  
Vol 104 ◽  
pp. 106244 ◽  
Author(s):  
Lixi Wen ◽  
Sitong Chen ◽  
Vicenţiu D. Rădulescu
Keyword(s):  
Poisson System ◽  
Axially Symmetric ◽  
Zero Mass

scholarly journals Existence of axially symmetric solutions for a kind of planar Schrödinger-Poisson system

2021 ◽  
Vol 6 (7) ◽  
pp. 7833-7844
Author(s):  
Qiongfen Zhang ◽  
◽  
Kai Chen ◽  
Shuqin Liu ◽  
Jinmei Fan ◽  
...  
Keyword(s):  
Poisson System ◽  
Axially Symmetric

scholarly journals Axially symmetric static sources: A general framework and some analytical solutions

2013 ◽  
Vol 87 (2) ◽  
Author(s):  
L. Herrera ◽  
A. Di Prisco ◽  
J. Ibáñez ◽  
J. Ospino
Keyword(s):  
Analytical Solutions ◽  
General Framework ◽  
Axially Symmetric

scholarly journals Existence of axially symmetric solutions for a kind of planar Schr\”{o}dinger-Poisson system

2021 ◽  
Author(s):  
Qiongfen Zhang ◽  
Kai Chen ◽  
Jinmei Fan ◽  
Shuqin Liu
Keyword(s):  
Symmetric Solution ◽  
Symmetric Functions ◽  
Poisson System ◽  
Axially Symmetric ◽  
Planar System ◽  
Variational Framework

In this paper, we study the following kind of Schr\”{o}dinger-Poisson system in ${\R}^{2}$ \begin{equation*} \left\{\begin{array}{ll} -\Delta u+V(x)u+\phi u=K(x)f(u),\ \ \ x\in{\R}^{2},\\ -\Delta \phi=u^{2},\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x\in{\R}^{2}, \end{array}\right. \end{equation*} where $f\in C({\R}, {\R} )$, $V(x)$ and $K(x)$ are both axially symmetric functions. By constructing a new variational framework and using some new analytic techniques, we obtain an axially symmetric solution for the above planar system. our result improves and extends the existing works.

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