00-71 Bernard Helffer and Mathieu Dutour
On bifurcations from normal solutions for superconducting states (60K, latex) Feb 12, 00
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Abstract. Motivated by the paper by J.~Berger and K.~Rubinstein \cite{BeRu} and other recent studies \cite{GiPh}, \cite{LuPa1}, \cite{LuPa2}, we analyze the Ginzburg-Landau functional in an open bounded set $\Omega$. We mainly discuss the bifurcation problem whose analysis was initiated in \cite{Od} and show how some of the techniques developed by the first author in the case of Abrikosov's superconductors \cite{Du} can be applied in this context. In the case of non simply connected domains, we come back to \cite{BeRu} and \cite{HHOO}, \cite{HHOO1} for giving the analysis of the structure of the nodal sets for the bifurcating solutions.

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