TY - JOUR
T1 - Multiple Axially Asymmetric Solutions  to  a Mean Field Equation on $\mathbb{S}^{2}$
AU - Du , Zhuoran
AU - Gui , Changfeng
AU - Jin , Jiaming
AU - Li , Yuan
JO - Analysis in Theory and Applications
VL - 1
SP - 19
EP - 32
PY - 2020
DA - 2020/05
SN - 36
DO - http://doi.org/10.4208/ata.OA-0016
UR - https://global-sci.org/intro/article_detail/ata/16911.html
KW - Mean field equation, axially asymmetric solutions, bifurcation.
AB - <p style="text-align: justify;">We study the following mean field equation</p><p style="text-align: justify;">$$\Delta_{g}u+\rho\left(\frac{e^{u}}{\int_{\mathbb{S}^{2}}e^{u}d\mu}-\frac{1}{4\pi}\right)=0\ \&nbsp; \mbox{in}\ \ \mathbb{S}^{2},$$</p><p style="text-align: justify;">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&nbsp; odd integer $n\geq3$.</p>