Symmetric Solutions Of A Differential System Related To The One-Dimensional Ginzburg-Landau Models Of Superconductivity With S-N-S Junctions

We study asymptotic behaviors of solutions for a differential system related to the one-dimensional Ginzburg-Landau models with S-N-S junctions,a sample in which a thin layer of normal materials is sandwiched between layers of superconducting materials, we prove that the limit of solutions are the solutions of a nonlinear ordinary differential equations as Ginzburg-Landau parameter tends to infinity. Moreover we investigate the structure of the symmetric solutions of the above nonlinear ordinary differential equations and find that the differential system may has one or two or three symmetric solution according to various conditions of related parameters.