Positive Ground State Solutions for Schrödinger-Poisson System with General Nonlinearity and Critical Exponent

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

Author Details

Qingfang Chen

Jiafeng Liao