  We consider a generalization of abelian Chern-Simons-Higgs model by
introducing a nonstandard kinetic term. In particular we show that the
Bogomolnyi equations of the abelian Higgs theory may be obtained, being its
solutions Nielsen-Olesen vortices with electric charge. In addition we study
the self-duality equations for a generalized non-relativistic
Maxwell-Chern-Simons model.
