  We show that the principle "nonvanishing of spectral flow of the
linearization along the trivial branch entails bifurcation of nontrivial
solutions ", proved in \cite{FPR} for critical points of one parameter families
of $C^2$ functionals with Fredholm Hessian, holds true for variational
perturbations of paths of unbounded self-adjoint Fredholm operators with a
fixed domain.
