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 R-2 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.