  The Extended BP (EBP) Generalized EXIT (GEXIT) function introduced in
\cite{MMRU05} plays a fundamental role in the asymptotic analysis of sparse
graph codes. For transmission over the binary erasure channel (BEC) the
analytic properties of the EBP GEXIT function are relatively simple and well
understood. The general case is much harder and even the existence of the curve
is not known in general. We introduce some tools from non-linear analysis which
can be useful to prove the existence of EXIT like curves in some cases. The
main tool is the Krasnoselskii-Rabinowitz (KR) bifurcation theorem.
