 04178 Pierre Del Castillo
 Existence and localization of solutions of the one dimensional GinzburgLandau system
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Jun 4, 04

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Abstract. Following \cite{BoFoHe1999,BoHe2002}, we construct subsolutions and supersolutions for the one dimensional GinzburgLandau 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 GinzburgLandau 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.
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