Minimizers Of A Kind Of Nonlinear Functionals

This paper is devoted to the study on the minimizers of a kind of nonlinear functionals.This kind of functionals is the limit of one-dimensional Ginzburg-Landau model of superconductivity with normal impurity inclusion as the Ginzburg-Landau parameter tends to infinity. The functionals have more than one critical points according to various conditions of related parameters. We establish a method to identify the minimizers and find the exact number of the minimizer on various relations of the parameters.