Extrapolation and inhornogeneous retarded differential equations on infinite dimensional spaces

  • L. Maniar
  • A. Rhandi


Using the extrapolation spaces introduced by Da Prato-Grisvard and Nagel, we prove the well-posedness of a more general inhomogenous retarded differential equation on infinite dimensional spaces.


Functional Differential Equation Abstract Cauchy Problem Infinite Dimensional Space Integrate Semigroup Unique Mild Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. [1]
    Adimy M., Ezzinbi K.,Integrated semigroups and Functional differential equation in infinite dimension space. Preprint.Google Scholar
  2. [2]
    Amman H.Linear and Quasilinear Parabolic Problems, Birkhäuser, Berlin 1995.Google Scholar
  3. [3]
    Clément Ph., Diekmann O., Gyllenberg M., Heijmans H.J.A.M., Thieme H.R.,Perturbation theory for dual semigroups, Part I: The sun-reflexive case. Math. Ann.277 (1987), 709–725.MATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    Clément Ph., Diekmann O., Gyllenberg M., Heijmans H.J.A.M., Thieme H.R.,Perturbation theory for dual semigroups, Part II: Timedependent perturbations in the sun-reflexive case. Proc. Roy. Soc. Edinb109 A (1988), 145–172.Google Scholar
  5. [5]
    Clément Ph., al.,One-Parameter Semigroups. CWI Monographs 5, Amesterdam, 1987.Google Scholar
  6. [6]
    Da Prato G., Grisvard E.,On extrapolation spaces, Rend. Accad. Naz. Lincei.72 (1982), 330–332.MATHGoogle Scholar
  7. [7]
    Hale J.K.,Theory of Functional Differential Equations, Springer-Verlag, 1977.Google Scholar
  8. [8]
    Hille E., Philips R.S.,Functional Analysis and Semigroups. Amer. Math. Soc.. Providence 1975.Google Scholar
  9. [9]
    Maniar L.,Equations différentielles à retard par la méthode d’extrapolation. Portugaliae Mathematica, to appear.Google Scholar
  10. [10]
    Nagel R.,One-Parameter Semigroups of Positive Operators. Lecture Notes1184, Springer-Verlag, 1986.Google Scholar
  11. [11]
    Nagel R.,Sobolev spaces and semigroups. Semesterbericht Funktionalanalysis, Band4 (1983), 1–20.Google Scholar
  12. [12]
    Nagel R., Sinestrari E.,Inhomogeneous Volterra integrodifferential equations for Hille-Yosida operators, Marcel Dekker, Lecture Notes Pure Appl. Math.150 (1994), 51–70.MathSciNetGoogle Scholar
  13. [13]
    van Neerven J.,The Adjoint of a Semigroup of Linear Operators. Lecture Notes Math.1529, Springer-Verlag, 1992.Google Scholar
  14. [14]
    Nickel G., Rhandi A.,On the essential spectral radius of semigroups generated by perturbations of Hille-Yosida operators. Diff. Integ. Equat., to appear.Google Scholar
  15. [15]
    Pazy A.,Semigroups of Linear Operators and Applications to Partial Differential Equations. Springer-Verlag, 1983.Google Scholar
  16. [16]
    Rhandi A.,Extrapolations methods to solve non-autonomous retarded differential equations. Studia Math.,126 (3) (1997), 219–233.MathSciNetGoogle Scholar
  17. [17]
    Rhandi A.,Positivity and stability of a population equation with diffusion on L 1. Positivity, to appear.Google Scholar
  18. [18]
    Walter T.,Störungstheorie von Generatoren und Favard-Klassen. Dissertation, Tübingen, 1986.Google Scholar

Copyright information

© Springer 1998

Authors and Affiliations

  • L. Maniar
    • 1
  • A. Rhandi
    • 1
  1. 1.Département de Mathématiques Faculté des Sciences SemlaliaUniversité Cadi AyyadMarrakechMaroc

Personalised recommendations