In this paper we are devoted to proving the existence and nonexistence of s
elf-dual equations arising in Chern-Simons-Higgs theory with a constant ele
ctric charge density. There are three kinds of boundary conditions that adm
it solitonic structures. It is shown that there exist solutions in two case
s of them. In the other case, we prove that there is a critical electric ch
arge density with negative value such that above the value there exists a s
olution and below it we have no solution. We also study asymptotic behavior
s for solutions as the electric charge density goes to zero. It is found th
at they converge to solutions of a topological Chern-Simons system without
constant electric charge density. (C) 1999 American Institute of Physics. [
S0022-2488(99)01801-0].