Resolvent of nonautonomous linear delay functional differential equations

Joël Blot; Mamadou I. Koné

Nonautonomous Dynamical Systems (2015)

  • Volume: 2, Issue: 1, page 77-101, electronic only
  • ISSN: 2353-0626

Abstract

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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.

How to cite

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Joël Blot, and Mamadou I. Koné. "Resolvent of nonautonomous linear delay functional differential equations." Nonautonomous Dynamical Systems 2.1 (2015): 77-101, electronic only. <http://eudml.org/doc/276541>.

@article{JoëlBlot2015,
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.},
author = {Joël Blot, Mamadou I. Koné},
journal = {Nonautonomous Dynamical Systems},
keywords = {resolvent; linear delay functional differential equation},
language = {eng},
number = {1},
pages = {77-101, electronic only},
title = {Resolvent of nonautonomous linear delay functional differential equations},
url = {http://eudml.org/doc/276541},
volume = {2},
year = {2015},
}

TY - JOUR
AU - Joël Blot
AU - Mamadou I. Koné
TI - Resolvent of nonautonomous linear delay functional differential equations
JO - Nonautonomous Dynamical Systems
PY - 2015
VL - 2
IS - 1
SP - 77
EP - 101, electronic only
AB - 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.
LA - eng
KW - resolvent; linear delay functional differential equation
UR - http://eudml.org/doc/276541
ER -

References

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  16. [16] S.-I. Nakagiri, Structural properties of functional differential equations in Banach spaces, Osaka J.Math. 25 (1988), 353-398.  Zbl0713.34069
  17. [17] E. Ramis, C. Deschamps, and J. Odoux, Cours de mathématiques spéciales; tome 3: topologie et éléments d’analyse, Third edition, Masson, Paris, 1991.  Zbl0471.00002
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