Existence and bifurcation theorems for the Ginzburg-Landau equations

The second-order transition of a superconducting material from normal to superconducting state according to the Ginzburg-Landau theory is rigorously discussed. The bifurcation of a superconducting state is proved for both the Abrikosov mixed state and the case of a film in a parallel magnetic field when the flux or external field is slightly less than critical. The existence of a mixed state for all values of flux below the critical value is also proved.