Positive Ground State Solutions for Schrödinger-Poisson System with General Nonlinearity and Critical Exponent
Year: 2023
Author: Qingfang Chen, Jiafeng Liao
Journal of Partial Differential Equations, Vol. 36 (2023), Iss. 1 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jpde.v36.n1.5
Journal of Partial Differential Equations, Vol. 36 (2023), Iss. 1 : pp. 68–81
Published online: 2023-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 14
Keywords: Schrödinger-Poisson system