  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.
