  We study Ginzburg-Landau equations for a complex vector order parameter. We
consider the Dirichlet problem in the disk in the plane with a symmetric,
degree-one boundary condition, and study its stability, in the sense of the
spectrum of the second variation of the energy. We find that the stability of
the degree-one equivariant solution depends on both the Ginzburg-Landau
parameter as well as the sign of the interaction term in the energy.
