Multiplicity for a nonlinear fourth-order elliptic equation in Maxwell-Chern-Simons vortex theory

Abstract

We prove the existence of at least two solutions for a fourth-order equation, which includes the vortex equations for the $U(1)$ and $CP(1)$ self-dual Maxwell-Chern-Simons models as special cases. Our method is variational, and it relies on an ``asymptotic maximum principle" property for a special class of supersolutions to this fourth-order equation.