Remarks on nontopological solutions in the self-dual Chern-Simons gauged $O(3)$ sigma models
Bull. Korean Math. Soc. 2016 Vol. 53, No. 3, 765-777
Published online May 31, 2016
Nari Choi and Jongmin Han
Kyung Hee University, Kyung Hee University
Abstract : 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 \cite{CH13R2, CH11, CHLLi}. We prove the existence of solutions in this case when there are only vortex points. Moreover, if $-1\le \tau<1$, we establish solutions which are perturbed from the solutions of singular Liouville equations.
Keywords : Chern-Simons gauged $O(3)$ sigma model, nontopological solu\-tions
MSC numbers : Primary 81T13, 35B40
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