A principle of linearized stability is given for the abstract functional differential equation
,
,
, where B generates a strongly continuous semigroup of bounded linear operators on a Banach space X, and
is a nonlinear, continuously Frechet-differentiable operator. The strong positivity property of irreducibility is
... [Show full abstract] also investigated for the semigroup associated with solutions of the linearized equation. The theory is applied to the stability analysis of an equation from population dynamics.