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 - <p style="text-align: justify;">In this paper, we consider the following Schrödinger-Poisson system \begin{equation*}\begin{cases} -\Delta u + \eta\phi u = f(x,u) + u^5,&amp; x\in\Omega,\\ -\Delta\phi=u^2,&amp; x\in\Omega,\\u = \phi =0,&amp; 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.</p>