- 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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