On the Chern–Simons–Higgs vortex equation without gauge fields

This paper is concerned with the nonself-dual Chern–Simons–Higgs model on R2R2 with vanishing gauge fields. We prove the existence of radial solutions with the topological boundary condition, and the nonexistence of radial solutions with the nontopological boundary condition. We also establish the asymptotic properties of solutions and derive the quantization of the potential energy.