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Nonautonomous Dynamical Systems

formerly Nonautonomous and Stochastic Dynamical Systems

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Resolvent of nonautonomous linear delay functional differential equations

Joël Blot
  • Laboratoire SAMM, Université Paris 1 Panthéon-Sorbonne, centre P.M.F., 90 rue de Tolbiac, 75634 Paris cedex 13, France,
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Mamadou I. Koné
  • Laboratoire SAMM, Université Paris 1 Panthéon-Sorbonne, centre P.M.F., 90 rue de Tolbiac, 75634 Paris cedex 13, France,
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2015-10-16 | DOI: https://doi.org/10.1515/msds-2015-0006

Abstract

The aim of this paper is to give a complete proof of the formula for the resolvent of a nonautonomous linear delay functional differential equations given in the book of Hale and Verduyn Lunel [9] 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.

Keywords: resolvent; linear delay functional differential equation

References

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About the article

Received: 2015-06-15

Accepted: 2015-09-24

Published Online: 2015-10-16


Citation Information: Nonautonomous Dynamical Systems, ISSN (Online) 2353-0626, DOI: https://doi.org/10.1515/msds-2015-0006.

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©2015 Joël Blot and Mamadou I. Koné. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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