  In the field of Energy Density Functionals (EDF) used in nuclear structure
and dynamics, one of the unsolved issues is the stability of the functional.
Numerical issues aside, some EDFs are unstable with respect to particular
perturbations of the nuclear ground-state density. The aim of this contribution
is to raise questions about the origin and nature of these instabilities, the
techniques used to diagnose and prevent them, and the domain of density
functions in which one should expect a nuclear EDF to be stable.
