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.