Translator Disclaimer
November/December 2020 On the planar Schrödinger-Poisson system with zero mass and critical exponential growth
Sitong Chen, Xianhua Tang
Adv. Differential Equations 25(11/12): 687-708 (November/December 2020).

Abstract

This paper is concerned with the following planar Schrödinger-Poisson system with zero mass \begin{equation*} \begin{cases} -\Delta u+\lambda \phi u=f(x,u), \;\; & x\in {\mathbb R}^{2},\\ \Delta \phi=2\pi u^2, \;\; & x\in {\mathbb R}^{2}, \end{cases} \end{equation*} where $\lambda > 0$ and $f\in \mathcal{C}(\mathbb R^2\times\mathbb R, \mathbb R)$ is of subcritical or critical exponential growth in the sense of Trudinger-Moser. By using some new analytical approaches, we prove that the above system has axially symmetric solutions under weak assumptions on $\lambda$ and $f$. This seems the first result on the planar Schrödinger-Poisson system with zero mass.

Citation

Download Citation

Sitong Chen. Xianhua Tang. "On the planar Schrödinger-Poisson system with zero mass and critical exponential growth." Adv. Differential Equations 25 (11/12) 687 - 708, November/December 2020.

Information

Published: November/December 2020
First available in Project Euclid: 12 November 2020

MathSciNet: MR4173173

Subjects:
Primary: 35J20, 35J62, 35Q55

Rights: Copyright © 2020 Khayyam Publishing, Inc.

JOURNAL ARTICLE
22 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.25 • No. 11/12 • November/December 2020
Back to Top