  We investigate the relevance of the conformal method by investigating
stability issues for the Einstein-Lichnerowicz conformal constraint system in a
nonlinear scalar-field setting. We prove the stability of the system with
respect to arbitrary perturbations of generic focusing physics data on closed
locally conformally flat manifolds, in any dimension. We also show that our
stability result is sharp by constructing explicit instability examples when
its assumptions are not satisfied. Our results apply to a more general class of
constraint-like systems.
