We consider the bifurcating solutions for the Ginzburg–Landau equations when the
superconductor is a film of thickness 2d submitted to an external magnetic field.
We refine some results obtained earlier [1] on the stability of bifurcating solutions
starting from normal solutions. We prove, in particular, the existence of curves
d [map ] κ0(d), defined for large d and tending to
2−1/2 when d [map ] +∞ and
κ [map ] d1(κ), defined for small κ and tending to
√5/2 when κ [map ] 0, which separate the sets of pairs
(κ, d) corresponding to different behaviour of the symmetric
bifurcating solutions. In this way, we give in particular a complete answer to the question of
stability of symmetric bifurcating solutions in the asymptotics ‘κ
fixed-d large’ or ‘d fixed-κ small’.