Anal. Theory Appl., 36 (2020), pp. 19-32.
Published online: 2020-05
[An open-access article; the PDF is free to any online user.]
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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 = {http://global-sci.org/intro/article_detail/ata/16911.html} }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 $n\geq3$.