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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  1. [1] M. Adimy, Integrated semigroups and delay differential equations, J. Math. Anal. Appl. 177 (1993), 125-134.  Zbl0776.34045
  2. [2] J.-P. Aubin, Abstract and applied analysis, Wiley-Interscience, New York, 1977.  
  3. [3] H.T. Banks, Representation of solutions of linear functional differential equations, Differential Equations 5 (1969), 399-409.  Zbl0165.42701
  4. [4] J. Blot, On the almost everywhere continuity, arXiv: 1411.3582v1[math.OC] 13 Nov 2014.  
  5. [5] L. Chambadal, and J.-L. Ovaert, Cours de mathématiques; tome 2 : analyse II, Gauthier-Villars, Paris, 1972.  Zbl0239.26001
  6. [6] J. Dieudonné, Éléments d’analyse; tome 1: fondements de l’analyse moderne, French edition, Gauthier-Villars, Paris, 1969.  
  7. [7] W. Fleming, Functions of several variables, Springer-Verlag, New York, 1977.  Zbl0348.26002
  8. [8] J. Genet, Mesure et intégration, Librairie Vuibert, Paris, 1976.  
  9. [9] J.K. Hale, and M.S. Verduyn Lunel, Introduction to functional differential equations, Springer-Verlag, New York, 1991.  
  10. [10] H. Helson, Harmonic analysis, Wadsworth, Inc., Belmont, California, 1991.  Zbl0837.43001
  11. [11] L.V. Kantorovitch, and G.P. Akilov, Analyse fonctionnelle, tome 1: opérateurs et fonctionnelles linéaires, French edition, MIR, Moscow, 1981.  
  12. [12] A.N. Kolmogorov, and S.V. Fomin, Éléments de la théorie des fonctions et de l’analyse fonctionnelle, French edition, MIR, Moscow, 1974.  
  13. [13] S. Lang, Real and functional analysis, Third edition, Springer-Verlag, New York, 1983.  
  14. [14] L.A. Liusternik, and V.J. Sobolev, Elements of functional analysis, English edition, Frederick Ungar Publishing Co., New York, 1961.  
  15. [15] L. Maniar, Équations différentielles à retard par la méthode d’extrapolation, Port. Math. 54 (1997), 101-113.  Zbl0876.34072
  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
  18. [18] E. Ramis, C. Deschamps, and J. Odoux, Cours de mathématiques spéciales; tome 4: séries et équations différentielles, Third edition, Masson, Paris, 1977.  Zbl0471.00003
  19. [19] F. Riesz and B. Sz. Nagy, Leçons d’analyse fonctionnelle, Sixth edition, Gauthier-Villars, Paris, 1975.  
  20. [20] W. Rudin, Real and complex analysis, McGraw-Hill Book Comp., Singapore, 1987.  Zbl0925.00005

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