Ginzburg–Landau Equation with DeGennes Boundary Condition

We study the asymptotic behavior of the positive solutions of the Ginzburg–Landau equation with the DeGennes boundary condition. This problem is closely related to the mathematical theory for superconductivity. We obtain the precise profile of boundary layer of the solutions and the estimates of their energy. These results are based on the uniqueness of positive solution of the limiting problem, which seems to be of independent interest.