Existence and non-existence of solutions of the mean field equations on flat tori
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- by Zhijie Chen, Ting-Jung Kuo and Chang-Shou Lin PDF
- Proc. Amer. Math. Soc. 145 (2017), 3989-3996 Request permission
Abstract:
We prove the existence or non-existence of solutions of the mean field equation (1.1) with $n=1$ or $n=2$ for a rectangular torus $E$. It is interesting to see that the results depend on the location of the half period $\frac {\omega _{k}}{2}$.References
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Additional Information
- Zhijie Chen
- Affiliation: Department of Mathematical Sciences, Yau Mathematical Sciences Center, Tsinghua University, Beijing, 100084, People’s Republic of China
- MR Author ID: 942005
- Email: zjchen@math.tsinghua.edu.cn
- Ting-Jung Kuo
- Affiliation: Taida Institute for Mathematical Sciences (TIMS), National Taiwan University, Taipei 10617, Taiwan
- Address at time of publication: Department of Mathematics, National Taiwan Normal University, Taipei 11677, Taiwan
- MR Author ID: 962054
- Email: tjkuo1215@ntnu.edu.tw
- Chang-Shou Lin
- Affiliation: Taida Institute for Mathematical Sciences (TIMS), Center for Advanced Study in Theoretical Sciences (CASTS), National Taiwan University, Taipei 10617, Taiwan
- MR Author ID: 201592
- Email: cslin@math.ntu.edu.tw
- Received by editor(s): October 7, 2016
- Received by editor(s) in revised form: October 18, 2016
- Published electronically: April 7, 2017
- Communicated by: Lei Ni
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 3989-3996
- MSC (2010): Primary 34M55, 35J15
- DOI: https://doi.org/10.1090/proc/13543
- MathSciNet review: 3665050