## A semi-elliptic system arising in the theory
of type-II superconductivity

### H. Berestycki, A. Bonnet
& S. J. Chapman

A reduced form of the Ginzburg-Landau equations of superconductivity is
considered, corresponding to the formal limit as the Ginzburg-Landau
parameter $\kappa$ tends to infinity.
Existence and uniqueness of the solution is established, up to the point at
which the magnitude of the potential first becomes equal to $1/\sqrt{3}$,
when the solution becomes linearly unstable. The instability
is shown to occur first on the boundary of the sample.
Finally a more complete study of one-dimensional and radially-symmetric
cases is presented.