Nonself-dual Chern–Simons and Maxwell–Chern–Simons vortices on bounded domains

We first show the existence of the multivortex solutions of Maxwell–Chern–Simons–Higgs (MCSH) model on bounded domains and prove that the solutions of the Euler–Lagrange equations of the MCSH energy functional converge to those of the Abelian–Higgs (AH) model and the Chern–Simons–Higgs (CSH) model in suitable limits, respectively. We also show the existence of the multivortex solutions of the nonself-dual CSH model on bounded domains. Besides, we study asymptotics for the minimizers of MCSH energy functional when the gauge field vanishes. © 2004 Elsevier Inc. All rights reserved.