  We study a boundary value problem associated with a system of two second
order differential equations with cubic nonlinearity which model a film of
superconductor material subjected to a tangential magnetic field. We show that
for an appropriate range of parameters there are {\it asymmetric} solutions,
and only trivial {\it symmetric} solutions. We then show that the associated
energy function is negative for the asymmetric solutions, and zero for the
trivial symmetric solution. It follows that a global minimizer of the energy is
asymmetric.
