On the global bifurcation diagram for the one-dimensional Ginzburg Landau model of superconductivity

Some new global results are given about solutions to the boundary value problem for the Euler-Lagrange equations for the Ginzburg-Landau model of a one-dimensional superconductor. The main advance is a proof that in some parameter range there is a branch of asymmetric solutions connecting the branch of symmetric solutions to the normal state. Also, simplified proofs are presented for some local bifurcation results of Bolley and Helffer. These proofs require no detailed asymptotics for the solutions of the linear equations. Finally, an error in Odeh's work on this problem is discussed.