full
search.png

Search

close.png

Cancel

arrow
Volume 36, Issue 1
Positive Ground State Solutions for Schrödinger-Poisson System with General Nonlinearity and Critical Exponent

Qingfang Chen & Jiafeng Liao

DOI: 10.4208/jpde.v36.n1.5

J. Part. Diff. Eq., 36 (2023), pp. 68-81.

Published online: 2022-12

Preview Full PDF 2151 29659

Cited by

google scholar semantic scholar
Export citation
  • Abstract

In this paper, we consider the following Schrödinger-Poisson system \begin{equation*}\begin{cases} -\Delta u + \eta\phi u = f(x,u) + u^5,& x\in\Omega,\\ -\Delta\phi=u^2,& x\in\Omega,\\u = \phi =0,& x\in \partial\Omega, \end{cases}\end{equation*} where $\Omega$ is a smooth bounded domain in $R^3$, $\eta=\pm1$ and the continuous function $f$ satisfies some suitable conditions. Based on the Mountain pass theorem, we prove the existence of positive ground state solutions.

  • Keywords

Schrödinger-Poisson system Sobolev critical exponent positive ground state solution Mountain pass theorem.

  • AMS Subject Headings

35B33, 35J20, 35J60

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

ncyz2012cqf@163.com (Qingfang Chen)

liaojiafeng@163.com (Jiafeng Liao)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-36-68, author = {Chen , Qingfang and Liao , Jiafeng}, title = {Positive Ground State Solutions for Schrödinger-Poisson System with General Nonlinearity and Critical Exponent}, journal = {Journal of Partial Differential Equations}, year = {2022}, volume = {36}, number = {1}, pages = {68--81}, abstract = {

In this paper, we consider the following Schrödinger-Poisson system \begin{equation*}\begin{cases} -\Delta u + \eta\phi u = f(x,u) + u^5,& x\in\Omega,\\ -\Delta\phi=u^2,& x\in\Omega,\\u = \phi =0,& x\in \partial\Omega, \end{cases}\end{equation*} where $\Omega$ is a smooth bounded domain in $R^3$, $\eta=\pm1$ and the continuous function $f$ satisfies some suitable conditions. Based on the Mountain pass theorem, we prove the existence of positive ground state solutions.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v36.n1.5}, url = {http://global-sci.org/intro/article_detail/jpde/21294.html} }
TY - JOUR T1 - Positive Ground State Solutions for Schrödinger-Poisson System with General Nonlinearity and Critical Exponent AU - Chen , Qingfang AU - Liao , Jiafeng JO - Journal of Partial Differential Equations VL - 1 SP - 68 EP - 81 PY - 2022 DA - 2022/12 SN - 36 DO - http://doi.org/10.4208/jpde.v36.n1.5 UR - https://global-sci.org/intro/article_detail/jpde/21294.html KW - Schrödinger-Poisson system KW - Sobolev critical exponent KW - positive ground state solution KW - Mountain pass theorem. AB -

In this paper, we consider the following Schrödinger-Poisson system \begin{equation*}\begin{cases} -\Delta u + \eta\phi u = f(x,u) + u^5,& x\in\Omega,\\ -\Delta\phi=u^2,& x\in\Omega,\\u = \phi =0,& x\in \partial\Omega, \end{cases}\end{equation*} where $\Omega$ is a smooth bounded domain in $R^3$, $\eta=\pm1$ and the continuous function $f$ satisfies some suitable conditions. Based on the Mountain pass theorem, we prove the existence of positive ground state solutions.

Chen , Qingfang and Liao , Jiafeng. (2022). Positive Ground State Solutions for Schrödinger-Poisson System with General Nonlinearity and Critical Exponent. Journal of Partial Differential Equations. 36 (1). 68-81. doi:10.4208/jpde.v36.n1.5
Copy to clipboard
BibteX RIS TXT
The citation has been copied to your clipboard