Existence and nonexistence in Chern-Simons-Higgs theory with a constant electric charge density

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].