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

Abstract

In this paper we are devoted to proving the existence and nonexistence of self-dual equations arising in Chern-Simons-Higgs theory with a constant electric charge density. There are three kinds of boundary conditions that admit solitonic structures. It is shown that there exist solutions in two cases of them. In the other case, we prove that there is a critical electric charge density with negative value such that above the value there exists a solution and below it we have no solution. We also study asymptotic behaviors for solutions as the electric charge density goes to zero. It is found that 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].