Multiplicity results for the two-vortex Chern-Simons Higgs model on the two-sphere

We consider a Ginzburg-Landau type functional on S-2 with a 6(th) order pot ential and the corresponding selfduality equations. We study the limiting b ehavior in the two vortex case when a coupling parameter tends to zero. Thi s two vortex case is a limiting case for the Moser inequality, and we corre spondingly detect a rich and varied asymptotic behavior depending on rile p osition of the vortices. We exploit analogies with the Nirenberg problem fo r the prescribed Gauss curvature equation on S-2.