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Self duality equations for Ginzburg-Landau and Seiberg-Witten type functionals with 6th order potentials. (English) Zbl 0994.58009
Summary: The abelian Chern-Simons-Higgs model of Hong-Kim-Pac and Jackiw-Weinberg leads to a Ginzburg-Landau type functional with a 6th order potential on a compact Riemann surface. We derive the existence of two solutions with different asymptotic behavior as the coupling parameter tends to 0, for any number of prescribed vortices. We also introduce a Seiberg-Witten type functional with a 6th order potential and again show the existence of two asymptotically different solutions on a compact Kähler surface. The analysis is based on maximum principle arguments and applies to a general class of scalar equations.

58E30 Variational principles in infinite-dimensional spaces
35J60 Nonlinear elliptic equations
53C99 Global differential geometry
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