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 $n\geq3$.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.OA-0016}, url = {https://global-sci.com/article/73805/multiple-axially-asymmetric-solutions-to-a-mean-field-equation-on-mathbbs2} }