Abstract
This paper concerns the Ginzburg-Landau equation and the Meissner equations on a bounded multiply-connected domain in R3. The novelty of these equations is that both of them contain an unknown potential and an unknown Neumann field as the Lagrange multipliers. The minimal and non-minimal solutions for each equation are obtained by variational methods, and the effect of the applied magnetic field on the Meissner states is examined. The Meissner A-system with potential is also examined and a solution is obtained by using the Mountain Pass Lemma of Ambrosetti and Rabinowitz. In our analysis the estimates of the natural boundary value problem of the Maxwell-Stokes system play an important role.
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