| Multiple Non-Axially Solutions to a Mean Field Equation on S^2 |
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| 作者姓名： | Zhuoran Du Changfeng Gui Jiaming Jin Yuan Li |
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| 作者单位： | School of Mathematics;Department of Mathematics |
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| 基金项目： | supported by the Natural Science Foundation of Hunan Province;China(Grant No.2016JJ2018);partially supported by NSF grants DMS-1601885 and DMS-1901914;Simons Foundation Award 617072。 |
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| 摘 要： | We study the following mean field equation■,whereρis a real parameter.We obtain the existence of multiple non-axially symmetric solutions bifurcating from u=0 at the valuesρ=4 n(n+1)πfor any odd integer n≥3.
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| 关 键 词： | Mean field equation non-axially solutions BIFURCATION |
Multiple Axially Asymmetric Solutions to a Mean Field Equation on $\mathbb{S}^{2}$ |
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| Zhuoran Du,Changfeng Gui,Jiaming Jin,Yuan Li.Multiple Non-Axially Solutions to a Mean Field Equation on S^2[J].Analysis in Theory and Applications,2020,36(1):19-32. |
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| Authors: | Zhuoran Du Changfeng Gui Jiaming Jin & Yuan Li |
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| 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 $n\geq3$. |
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| Keywords: | Mean field equation axially asymmetric solutions bifurcation |
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