Self duality equations for Ginzburg-Landau and Seiberg-Witten type functionals with 6(th) order potentials

The abelian Chern-Simons-Higgs model of Hong-Kim-Pac and Jackiw-Weinberg le ads to a Ginzburg-Landau type functional with a 6(th) order potential on a compact Riemann surface. We derive the existence of two solutions with diff erent asymptotic behavior as the coupling parameter tends to 0, for any num ber of prescribed vortices. We also introduce a Seiberg-Witten type functio nal with a 6(th) order potential and again show the existence of two asympt otically different solutions on a compact Kahler surface. The analysis is b ased on maximum principle arguments and applies to a general class of scala r equations.