Year: 2020
Author: Zhuoran Du, Changfeng Gui, Jiaming Jin, Yuan Li
Analysis in Theory and Applications, Vol. 36 (2020), Iss. 1 : pp. 19–32
Abstract
We study the following mean field equation
$$\Delta_{g}u+\rho\left(\frac{e^{u}}{\int_{\mathbb{S}^{2}}e^{u}d\mu}-\frac{1}{4\pi}\right)=0\ \ \mbox{in}\ \ \mathbb{S}^{2},$$
where $\rho$ is a real parameter. We obtain the existence of multiple axially asymmetric solutions bifurcating from $u=0$ at the values $\rho=4n(n+1)\pi$ for any odd integer $n\geq3$.
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.OA-0016
Analysis in Theory and Applications, Vol. 36 (2020), Iss. 1 : pp. 19–32
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 14
Keywords: Mean field equation axially asymmetric solutions bifurcation.
Author Details
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Some geometric inequalities related to Liouville equation
Gui, Changfeng
Li, Qinfeng
Mathematische Zeitschrift, Vol. 305 (2023), Iss. 3
https://doi.org/10.1007/s00209-023-03369-5 [Citations: 2]