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 <TEX>${\tau}{\in}[-1,1</TEX><TEX>]</TEX><TEX>$</TEX> appearing in the nonlinear term. The case <TEX>${\tau}=1$</TEX> 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 <TEX>$-1{\leq}{\tau}$</TEX><1, we establish solutions which are perturbed from the solutions of singular Liouville equations.

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