• Bulletin of the Korean Mathematical Society
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• v.53 no.3
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• pp.765-777
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• 2016

In this paper, we prove the existence of nontopological solutions to the self-dual equations arising from the Chern-Simons gauged O(3) sigma models. The property of solutions depends on a parameter ${\tau}{\in}[-1,1]$ appearing in the nonlinear term. The case ${\tau}=1$ lies on the borderline for the existence of solutions in the previous results [4, 5, 7]. We prove the existence of solutions in this case when there are only vortex points. Moreover, if $-1{\leq}{\tau}$<1, we establish solutions which are perturbed from the solutions of singular Liouville equations.

• Journal of the Korean Mathematical Society
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• v.44 no.4
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• pp.997-1012
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• 2007

We consider the nonrelativistic limit in the self-dual Abelian Chern-Simons model, and give a rigorous proof of the limit for the radial solutions to the self-dual equations with the nontopological boundary condition when there is only one-vortex point. By keeping the shooting constant of radial solutions to be fixed, we establish the convergence of radial solutions in the nonrelativistic limit.