Existence of axially symmetric solutions for a kind of planar Schrödinger-Poisson system
In this paper, we study the following kind of Schrödinger-Poisson system in $ { \mathbb{R}}^{2} $ $ \begin{equation*} \left\{\begin{array}{ll} -\Delta u+V(x)u+\phi u = K(x)f(u), \ \ \ x\in{ \mathbb{R}}^{2}, \\ \Delta \phi = u^{2}, \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \...
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| Format: | Article |
| Language: | English |
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AIMS Press
2021-05-01
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| Series: | AIMS Mathematics |
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| Online Access: | http://www.aimspress.com/article/doi/10.3934/math.2021455?viewType=HTML |
| _version_ | 1818766418779308032 |
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| author | Qiongfen Zhang Kai Chen Shuqin Liu Jinmei Fan |
| author_facet | Qiongfen Zhang Kai Chen Shuqin Liu Jinmei Fan |
| author_sort | Qiongfen Zhang |
| collection | DOAJ |
| description | In this paper, we study the following kind of Schrödinger-Poisson system in $ { \mathbb{R}}^{2} $
$ \begin{equation*} \left\{\begin{array}{ll} -\Delta u+V(x)u+\phi u = K(x)f(u), \ \ \ x\in{ \mathbb{R}}^{2}, \\ \Delta \phi = u^{2}, \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x\in{ \mathbb{R}}^{2}, \end{array}\right. \end{equation*} $
where $ f\in C({ \mathbb{R}}, { \mathbb{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. |
| first_indexed | 2024-12-18T08:33:41Z |
| format | Article |
| id | doaj.art-30db96b7deec483e8d3139da24e7df34 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-18T08:33:41Z |
| publishDate | 2021-05-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-30db96b7deec483e8d3139da24e7df342022-12-21T21:14:23ZengAIMS PressAIMS Mathematics2473-69882021-05-01677833784410.3934/math.2021455Existence of axially symmetric solutions for a kind of planar Schrödinger-Poisson systemQiongfen Zhang0Kai Chen1Shuqin Liu2Jinmei Fan 31. School of Science, Guilin University of Technology, Guilin, Guangxi 541004, China2. School of Science, Guilin University of Aerospace Technology, Guilin, Guangxi 541004, China1. School of Science, Guilin University of Technology, Guilin, Guangxi 541004, China1. School of Science, Guilin University of Technology, Guilin, Guangxi 541004, ChinaIn this paper, we study the following kind of Schrödinger-Poisson system in $ { \mathbb{R}}^{2} $ $ \begin{equation*} \left\{\begin{array}{ll} -\Delta u+V(x)u+\phi u = K(x)f(u), \ \ \ x\in{ \mathbb{R}}^{2}, \\ \Delta \phi = u^{2}, \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x\in{ \mathbb{R}}^{2}, \end{array}\right. \end{equation*} $ where $ f\in C({ \mathbb{R}}, { \mathbb{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.http://www.aimspress.com/article/doi/10.3934/math.2021455?viewType=HTMLexistenceaxially symmetricground state solutionlogarithmic convolution potentialplanar schrödinger-poisson system |
| spellingShingle | Qiongfen Zhang Kai Chen Shuqin Liu Jinmei Fan Existence of axially symmetric solutions for a kind of planar Schrödinger-Poisson system AIMS Mathematics existence axially symmetric ground state solution logarithmic convolution potential planar schrödinger-poisson system |
| title | Existence of axially symmetric solutions for a kind of planar Schrödinger-Poisson system |
| title_full | Existence of axially symmetric solutions for a kind of planar Schrödinger-Poisson system |
| title_fullStr | Existence of axially symmetric solutions for a kind of planar Schrödinger-Poisson system |
| title_full_unstemmed | Existence of axially symmetric solutions for a kind of planar Schrödinger-Poisson system |
| title_short | Existence of axially symmetric solutions for a kind of planar Schrödinger-Poisson system |
| title_sort | existence of axially symmetric solutions for a kind of planar schrodinger poisson system |
| topic | existence axially symmetric ground state solution logarithmic convolution potential planar schrödinger-poisson system |
| url | http://www.aimspress.com/article/doi/10.3934/math.2021455?viewType=HTML |
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