# Doubly periodic self-dual vortices in a relativistic non-Abelian Chern–Simons model

@article{Han2012DoublyPS,
title={Doubly periodic self-dual vortices in a relativistic non-Abelian Chern–Simons model},
author={X. Han and G. Tarantello},
journal={Calculus of Variations and Partial Differential Equations},
year={2012},
volume={49},
pages={1149-1176}
}
• Published 2012
• Physics, Mathematics
• Calculus of Variations and Partial Differential Equations
In this paper we establish a multiplicity result concerning the existence of doubly periodic solutions in a $$2\times 2$$ nonlinear elliptic system arising in the study of self-dual non-Abelian Chern–Simons vortices. We show that the system admits at least two solutions when the Chern–Simons coupling parameter $$\kappa >0$$ is sufficiently small; while no solution exists for $$\kappa >0$$ sufficiently large. As in Nolasco and Tarantello (Commun Math Phys 213:599–639, 2000), we use a variational… Expand
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