### 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 (Formula Presented.).

Original language | English |
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Pages (from-to) | 3989-3996 |

Number of pages | 8 |

Journal | Proceedings of the American Mathematical Society |

Volume | 145 |

Issue number | 9 |

DOIs | |

Publication status | Published - 2017 Jan 1 |

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

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## Cite this

Chen, Z., Kuo, T-J., & Lin, C. S. (2017). Existence and non-existence of solutions of the mean field equations on flat tori.

*Proceedings of the American Mathematical Society*,*145*(9), 3989-3996. https://doi.org/10.1090/proc/13543