### 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 |
---|---|

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 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Proceedings of the American Mathematical Society*,

*145*(9), 3989-3996. https://doi.org/10.1090/proc/13543

**Existence and non-existence of solutions of the mean field equations on flat tori.** / Chen, Zhijie; Kuo, Ting Jung; Lin, Chang Shou.

Research output: Contribution to journal › Article

*Proceedings of the American Mathematical Society*, vol. 145, no. 9, pp. 3989-3996. https://doi.org/10.1090/proc/13543

}

TY - JOUR

T1 - Existence and non-existence of solutions of the mean field equations on flat tori

AU - Chen, Zhijie

AU - Kuo, Ting Jung

AU - Lin, Chang Shou

PY - 2017

Y1 - 2017

N2 - 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.).

AB - 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.).

UR - http://www.scopus.com/inward/record.url?scp=85021431451&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85021431451&partnerID=8YFLogxK

U2 - 10.1090/proc/13543

DO - 10.1090/proc/13543

M3 - Article

VL - 145

SP - 3989

EP - 3996

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 9

ER -