Bernard Helffer and Mathieu Dutour
On bifurcations from normal solutions for superconducting states
(60K, latex)

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.