Abstract
In this article, a planar relativistic self-dual Chern–Simons model with two Higgs particles and two gauge fields is considered. The main purpose is to show the existence of the nontopological multivortex solutions to the system from a mathematical perspective. Specifically, a certain type of nontopological solutions can be constructed by means of an approach of perturbation from the radially symmetric solutions of a Liouville system. These radial Liouville solutions are well depicted in terms of their asymptotic behavior prescribed at infinity. Accordingly, the values of charges and energy in response to the resulting nontopological solutions accumulate in the way that the Liouville solutions are characterized.
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