In this chapter, we establish the existence of multiple branches of stable solutions of (GL) which have an arbitrary number of vortices n, with both n bounded and n unbounded, but not too large, in a wide regime of applied fields. These solutions are obtained by minimizing the energy Gε over subsets Un of the functional space which correspond, very roughly speaking, to configurations with n vortices (or only allow for such when minimizing); the heart of the matter consists in proving that the minimum is achieved in the interior of Un, thus yielding locally minimizing solutions of the equations. These solutions turn out to be global energy minimizers in some narrow intervals of values of hex.


Narrow Sense Global Energy Minimizer Bibliographic Note Single Zero Total Radius 
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© Birkhäuser Boston 2007

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