Non-topological Multivortex Solutions to the Self-Dual Maxwell–Chern–Simons–Higgs Systems

In this paper we construct non-topological multivortex solutions to the non-relativistic self-dual Maxwell–Chern–Simons–Higgs system in R2 which make the energy functional finite. Moreover, our proof of the existence of solutions reveals precise asymptotic behavior of solutions near spatial infinity. Using exactly the same method, we also establish the existence of non-topological multivortex solutions to the relativistic self-dual Maxwell–Chern–Simons–Higgs system.