Bubbling solutions for a skew-symmetric Chern–Simons system in a torus

Xiaosen Han, Hsin-Yuan Huang *, Chang Shou Lin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We establish the existence of bubbling solutions for the following skew-symmetric Chern–Simons system {Δu1+[Formula presented]eu2(1−eu1)=4π∑i=1N1δpi1Δu2+[Formula presented]eu1(1−eu2)=4π∑i=1N2δpi2 over a parallelogram Ω with doubly periodic boundary condition, where ε>0 is a coupling parameter, and δp denotes the Dirac measure concentrated at p. We obtain that if (N1−1)(N2−1)>1, there exists an ε0>0 such that, for any ε∈(0,ε0), the above system admits a solution (u1,ε,u2,ε) satisfying u1,ε and u2,ε blow up simultaneously at the point p, and [Formula presented]euj,ε(1−eui,ε)→4πNiδp,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 languageEnglish
Pages (from-to)1354-1396
Number of pages43
JournalJournal of Functional Analysis
Volume273
Issue number4
DOIs
StatePublished - 15 Aug 2017

Keywords

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

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