Existence and asymptotics of topological solutions in the self-dual Maxwell–Chern–Simons O(3) sigma model

We are concerned with the topological vortex equations arising in the self-dual Maxwell–Chern–Simons O(3) sigma model. We prove the existence of solutions for any parameters κ and q by a variational method. We also verify both the Maxwell limit and the Chern–Simons limit for the variational solutions.