Stable configurations in superconductivity: Uniqueness, multiplicity, and vortex-nucleation

We find new stable solutions of the Ginzburg-Landau equation for high kappa superconductors with exterior magnetic field h(ex). First, we prove the un iqueness of the Meissner-type solution. Then, we prove, in the case of a di sc domain, the coexistence of branches of solutions with n vortices of degr ee one, for any n not too high and for a certain range of h(ex); and descri be these branches, Finally, we give an estimate on the nucleation energy ba rrier, to pass continuously from a vortexless configuration to a configurat ion with a centered vortex.