Abstract
This paper deals with a functional state-dependent delayed equation in which the delay is implicitly defined by a threshold condition. The equation originates in a class of age-structured population models in which the passage of individuals through the different stages of their life cycle occurs when some magnitude reaches a threshold value. The work analyses local existence of solutions, global existence of nonnegative solutions and uniqueness for smooth initial data. Some partial results on existence and stability of nonnegative stationary solutions are established through a linearized equation. This linearization is constructed from a differential formulation of the problem which is not equivalent to the original one, and the mathematical analysis is carried out in the setting of the C 0-semigroup theory.
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