Classification of the entire radial self-dual solutions to non-Abelian Chern-Simons systems

Hsin-Yuan Huang , Chang Shou Lin*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


We consider the entire radial solutions to the non-Abelian Chern-Simons systems of rank 2(δuδv)=-K(euev)+K(eu00ev)K(euev)+(4πN1δ04πN2δ0)(0.1)in R2, where Ni≥0, i=1, 2 and K=(aij) is a 2×2 matrix satisfying a11, a22>0, a12, a21<0 and a11a22-a12a21>0. This system is motivated by the relativistic non-Abelian Chern-Simons model, Lozano-Marqués-Moreno-Schaposnik model of bosonic sector of N=2 supersymmetric Chern-Simons-Higgs theory, and Gudnason model of N=2 supersymmetric Yang-Mills-Chern-Simons-Higgs theory. Understanding the structure of entire radial solutions is one of fundamental issues for the system of nonlinear equations. We prove that any entire radial solutions of (0.1) must be one of topological, non-topological and mixed type solutions, and completely classify the asymptotic behaviors at infinity of these solutions. As an application of this classification, we prove that the two components u and v have intersection at most finite times.

Original languageEnglish
Pages (from-to)6796-6841
Number of pages46
JournalJournal of Functional Analysis
Issue number12
StatePublished - 15 Jun 2014


  • Classification
  • Non-abelian chern-simons system
  • Non-topological solutions
  • Topological solutions

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