On the condensate multivortex solutions of the self-dual Maxwell-Chern-Simons CP(1) model

In this paper we prove the existence of periodic multivortex solutions in t he plane of the self-dual Maxwell-Chern-Simons CP(1) model where the kineti c part of the Lagrangian contains both Maxwell and Chern-Simons terms. We a lso study both of the Maxwell and the Chern-Simons limits. Finally we consi der the single signed vortex case and prove that the solutions are bounded from below or above by solutions of the Maxwell CP(1) model depending on th e sign of the vortices. As a simple corollary, in the vortex free case we c onstruct a unique explicit solution.