## Abstract

We establish the existence of bubbling solutions for the following skew-symmetric Chern–Simons system {Δu_{1}+[Formula presented]e^{u2}(1−e^{u1})=4π∑i=1N_{1}δ_{pi1}Δu_{2}+[Formula presented]e^{u1}(1−e^{u2})=4π∑i=1N_{2}δ_{pi2} over a parallelogram Ω with doubly periodic boundary condition, where ε>0 is a coupling parameter, and δ_{p} denotes the Dirac measure concentrated at p. We obtain that if (N_{1}−1)(N_{2}−1)>1, there exists an ε_{0}>0 such that, for any ε∈(0,ε_{0}), the above system admits a solution (u_{1,ε},u_{2,ε}) satisfying u_{1,ε} and u_{2,ε} blow up simultaneously at the point p^{⁎}, and [Formula presented]e^{uj,ε}(1−e^{ui,ε})→4πN_{i}δ_{p⁎},1≤i,j≤2,i≠j as ε→0, where the location of the point p^{⁎} defined by (1.12) satisfies the condition (1.13).

Original language | English |
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Pages (from-to) | 1354-1396 |

Number of pages | 43 |

Journal | Journal of Functional Analysis |

Volume | 273 |

Issue number | 4 |

DOIs | |

State | Published - 15 Aug 2017 |

## Keywords

- Bubbling solutions
- Non-degeneracy
- Skew-symmetric Chern–Simons system