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

We find new stable solutions of the Ginzburg-Landau equation for high κ superconductors with exterior magnetic field h_ex. First, we prove the uniqueness of the Meissner-type solution. Then, we prove, in the case of a disc domain, the coexistence of branches of solutions with n vortices of degree one, for any n not too high and for a certain range of h_ex; and describe these branches. Finally, we give an estimate on the nucleation energy barrier, to pass continuously from a vortexless configuration to a configuration with a centered vortex.