Semigroup Properties and the Crandall Liggett Approximation for a Class of Differential Equations with State-Dependent Delays

Abstract We present an approach for the resolution of a class of differential equations with state-dependent delays by the theory of strongly continuous nonlinear semigroups. We show that this class determines a strongly continuous semigroup in a closed subset of C 0, 1 . We characterize the infinitesimal generator of this semigroup through its domain. Finally, an approximation of the Crandall–Liggett type for the semigroup is obtained in a dense subset of ( C , ‖·‖ ∞ ). As far as we know this approach is new in the context of state-dependent delay equations while it is classical in the case of constant delay differential equations.