Resolvent of non autonomous linear delay functional differential equations.

Mamadou Ibrahima Koné (1) , Joël Blot (1)

1 SAMM - Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne)

The aim of this paper is to give a complete proof of the formula for the resolvent of a non autonomous linear delay functional differential equations given in the book of Hale and Verduyn Lunel under the assumption alone of the continuity of the right-hand side with respect to the time, when the notion of solution is a differentiable function at each point, which satisfies the equation at each point, and when the initial value is a continuous function.

Mots clés: Resolvent; linear delay functional differential equation.

Domaines: Optimisation et contrôle [math.OC]; Systèmes dynamiques [math.DS]

Mamadou Ibrahima Koné, Joël Blot. Resolvent of non autonomous linear delay functional differential equations.. Nonautonomous dynamical systems, 2015, 2, pp.77:101. ⟨hal-01337476⟩