New existence results for the mean field equation on compact surfaces via degree theory
New existence results for the mean field equation on compact surfaces via degree theory
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DOI：
10.4171/rsmup/136-2
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发表时间：
2014-09
期刊：
影响因子：
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通讯作者：
Aleks Jevnikar
中科院分区：
文献类型：
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作者：
Aleks Jevnikar
考虑紧致表面上一类具有指数非线性的方程，其形式为具有任意符号涡的平衡湍流的平均场方程。利用度理论证明了一个存在性结果。这在拓扑球的情况下得到了新的存在性结果。通过考虑与该问题相关的Leray-Schauder度的宇称进行了证明。用这种方法我们也恢复了一些已知的先前的结果。
We consider a class of equations with exponential non-linearities on a compact surface which arises as the mean field equation of the equilibrium turbulence with arbitrarily signed vortices. We prove an existence result via degree theory. This yields new existence results in case of a topological sphere. The proof is carried out by considering the parity of the Leray-Schauder degree associated to the problem. With this method we recover also some known previous results.