具有足够大 Ginzburg-Landau参数的一维Ginzburg-Landau超导方程组对称解的唯一性

UNIQUENESS OF SYMMETRIC SOLUTIONS FOR THE ONE-DIMENSIONAL GINZBURG-LANDAU EQUATIONS OF SUPERCONDUCTIVITY WITH HIGH KAPPA

本文证明了：当Ｇｉｎｚｂｕｒｇ－Ｌａｎｄａｕ参数足够大时，一维Ｇｉｎｚｂｕｒｇ－Ｌａｎｄａｕ超导方程组的对称解 是唯一的．该问题的难点在于所考虑的解具有“奇点”：也即，当Ｇｉｎｚｂｕｒｇ－Ｌａｎｄａｕ参数趋于无穷大 时，解的导数在这些点处趋于无穷．证明的关键是要得到解在这些奇点近旁的精细估计．

The uniqueness of symmetric solutions for the one-dimensional Ginzburg-Landau equa- tions of superconductivity is proved when the Ginzburg-Landau parameter is large enough. The difficulty of this problem is that the solutions have 'singular points' at which the deriva- tives of the solutions tend to infinity as the Ginzburg-Landau parameter does. The key to the proof is to get some careful estimates near the 'singular points'.