Pierre Del Castillo
Existence and localization of solutions of the one dimensional Ginzburg-Landau system
(372K, Postscript)
ABSTRACT. Following \cite{BoFoHe1999,BoHe2002}, we construct subsolutions and supersolutions for the one dimensional Ginzburg-Landau system on the bounded interval $[0,d]$ in the weak-$\ka$ limit and for $\ka d$ large. These constructions lead to a localization of positive solutions of the Ginzburg-Landau system satisfying $f(0)>\frac{1}{\sqrt 2}$. Then, using a minmax method \cite{Stur} and following \cite{alama} and \cite{Has1}, we deduce that there exist solutions which are not local minimizers of the relevant functional.