Existence and non-existence of solutions to the Ginzburg-Landau equations in a semi-infinite superconducting film

For the problem psi''/kappa(2) = psi(3) - psi + A(2)psi, A'' = psi(2)A, psi'(0) = psi(infinity) = 0, A'(0) = A'(infinity) = h, it is proved for type II superconductors (kappa > 1/root 2) that (1) No solutions can exist for h <= 1/root 2 other than the normal state psi &3bond; 0, A = hx + C; (2) Positive solutions (psi > 0) exist whenever 1/root 2 < h < h(c3) approximate to 1.7 kappa; (3) As h down arrow 1/root 2, the limit of any converging subsequence satisfies A = 0, 1 at infinity.