Non-topological solutions in the generalized self-dual Chern-Simons-Higgs theory

In this paper we construct a non-topological multivortex solution of a generalized version of the relativistic self-dual Chern-Simons-Higgs system in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${\Bbb R}^2$\end{document} that makes the energy functional finite. Our method of proof is an extension of the previous argument used by the authors to prove the existence of general type of non-topological multivortex solutions of the relativistic Chern-Simons-Higgs system, using an implicit function theorem argument with features similar to the Liapunov-Schmidt decomposition.