  In order to study electrically and magnetically charged vortices in
fractional quantum Hall effect and anyonic superconductivity, the
Maxwell-Chern-Simons (MCS) model was introduced by [Lee, Lee, Min (1990)] as a
unified system of the classical Abelian-Higgs model (AH) and the Chern-Simons
(CS) model. In this article, the first goal is to obtain the uniform (CS) limit
result of (MCS) model with respect to the Chern-Simons parameter without any
restriction on either a particular class of solutions or the number of vortex
points. The most important step for this purpose is to derive the relation
between the Higgs field and the neutral scalar field. Our (CS) limit result
also provides the critical clue to answer the open problems raised by
[Ricciardi,Tarantello (2000)] and [Tarantello (2004)], and we succeed to
establish the existence of periodic Maxwell-Chern-Simons vortices satisfying
the concentrating property of the density of superconductive electron pairs.
Furthermore, we expect that the (CS) limit analysis in this paper would help to
study the stability, multiplicity, and bubbling phenomena for solutions of the
(MCS) model.
