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Delay Equations

  • Mimmo Iannelli
  • Andrea Pugliese
Chapter
  • 1.7k Downloads
Part of the UNITEXT book series (UNITEXT, volume 79)

Abstract

As we already noted at the beginning of  Chap. 2, the need of introducing delays in the description of natural phenomena was clearly stated early in the past century and a first important contribution was due to Vito Volterra in the field of the class of equations that, after him, are actually named Volterra Equations (see 7 and the brief historical review in 1). However, delay equations, in the case of concentrated delays as well as of distributed delays, in their classical form or in the abstract context of Functional Differential Equations, have an extensive development starting with the 1950's. This appendix is mainly designed to meet the needs arising in the context of the basic models discussed in  Chap. 2 and provides a minimal pathway through the subject. The reader may refer to 2, 3, 6 for a full treatment.

Keywords

Characteristic Equation Hopf Bifurcation Asymptotic Stability Functional Differential Equation Formal Series 
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.

References

  1. 1.
    Arino, O., Hbid, M.L. , Ait Dads, E. (Eds.): Delay Differential Equations and Applications. Springer, Netherlands (2006)zbMATHGoogle Scholar
  2. 2.
    Bellman, R., Cooke, K.L.: Differential-Difference Equations. Academic Press, New York (1963)zbMATHGoogle Scholar
  3. 3.
    Diekmann, O., van Gils, S.A., Lunel, S., Walther, H.O.: Delay Equations: Functional, Complex, and Nonlinear Analysis. Applied Mathematical Science 110, Springer, New York (1991)Google Scholar
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    Doetsch, G.: Introduction to the Theory and Application of the Laplace Transformation. Springer-Verlag, Berlin Heidelberg (1974)CrossRefzbMATHGoogle Scholar
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    Hale, J.K., Lunel, S.: Introduction to Functional Differential Equations. Applied Mathematical Science 99, Springer, New York (1993)Google Scholar
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    Gripenberg, G. , Londen, S-O., Staffans, O.: Volterra Integral and Functional Equations. Cambridge University Press, Cambridge (1990)CrossRefzbMATHGoogle Scholar
  7. 7.
    Volterra, V.: Lecons sur les Équations Intégrales et les Équations intégro-différentielles. Gauthier-Villars, Paris (1913)zbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Mimmo Iannelli
    • 1
  • Andrea Pugliese
    • 1
  1. 1.Department of MathematicsUniversity of TrentoItaly

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