On Impulsive Ordinary and Delay Differential Equations

  • François Dubeau
  • Jamila Karrakchou
  • Abdellatif Ouansafi
  • Abdeljalil Sakat
Part of the Advances in Computational Management Science book series (AICM, volume 4)

Abstract

Existence and uniqueness of the solution to ordinary and delay differential equations with infinitely many state-dependent impulses are considered. A simple transformation allows us to show that these problems are equivalent to problems without impulse. A fixed point approach is then applied for an appropriate norm.

Keywords

Functional Differential Equation Management Science Delay Differential Equation Order Ordinary Differential Equation Infinite Dimensional System 
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References

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    A. Bensoussan, G. Da Prato, M. Delfour and S. Mitter, “Representation and Control of Infinite Dimensional Systems”, Vol. 1, Birkhäuser, Boston, 1992.Google Scholar
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    F. Dubeau, “On first order ordinary differential equations with infinitely many state dependent impulses”, Differential Equations and Dynamical Systems, 5 (1997), 85–89.Google Scholar
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    J. K. Hale, “Theory of Functional Differential Equations”, Springer-Verlag, New York, 1977.CrossRefGoogle Scholar
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    V. Lakshmikanthan, D. Bainov and P. Simeonov, “Theory of Impulsive Differential Equations”, World Scientific, Singapore, 1989.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

  • François Dubeau
  • Jamila Karrakchou
  • Abdellatif Ouansafi
  • Abdeljalil Sakat

There are no affiliations available

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