04-178 Pierre Del Castillo

Existence and localization of solutions of the one dimensional Ginzburg-Landau system (372K, Postscript) Jun 4, 04

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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.

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