On a nonlinear elliptic system from Maxwell–Chern–Simons vortex theory

Abstract

We define an abstract nonlinear elliptic system, admitting a variational structure, and including the vortex equations for some Maxwell–Chern–Simons gauge theories as special cases. We analyze the asymptotic behavior of its solutions, and we provide a general simplified framework for the asymptotics previously derived in those special cases. As a byproduct of our abstract formulation, we also find some new qualitative properties of solutions.