Almost periodic solutions of neutral impulsive systems with periodic time-dependent perturbed delays

Valéry Covachev; Zlatinka Covacheva; Haydar Akça; Eada Al-Zahrani

Open Mathematics (2003)

  • Volume: 1, Issue: 3, page 292-314
  • ISSN: 2391-5455

Abstract

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A neutral impulsive system with a small delay of the argument of the derivative and another delay which differs from a constant by a periodic perturbation of a small amplitude is considered. If the corresponding system with constant delay has an isolated ω-periodic solution and the period of the delay is not rationally dependent on ω, then under a nondegeneracy assumption it is proved that in any sufficiently small neighbourhood of this orbit the perturbed system has a unique almost periodic solution.

How to cite

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Valéry Covachev, et al. "Almost periodic solutions of neutral impulsive systems with periodic time-dependent perturbed delays." Open Mathematics 1.3 (2003): 292-314. <http://eudml.org/doc/268878>.

@article{ValéryCovachev2003,
abstract = {A neutral impulsive system with a small delay of the argument of the derivative and another delay which differs from a constant by a periodic perturbation of a small amplitude is considered. If the corresponding system with constant delay has an isolated ω-periodic solution and the period of the delay is not rationally dependent on ω, then under a nondegeneracy assumption it is proved that in any sufficiently small neighbourhood of this orbit the perturbed system has a unique almost periodic solution.},
author = {Valéry Covachev, Zlatinka Covacheva, Haydar Akça, Eada Al-Zahrani},
journal = {Open Mathematics},
keywords = {34A37; 34K10},
language = {eng},
number = {3},
pages = {292-314},
title = {Almost periodic solutions of neutral impulsive systems with periodic time-dependent perturbed delays},
url = {http://eudml.org/doc/268878},
volume = {1},
year = {2003},
}

TY - JOUR
AU - Valéry Covachev
AU - Zlatinka Covacheva
AU - Haydar Akça
AU - Eada Al-Zahrani
TI - Almost periodic solutions of neutral impulsive systems with periodic time-dependent perturbed delays
JO - Open Mathematics
PY - 2003
VL - 1
IS - 3
SP - 292
EP - 314
AB - A neutral impulsive system with a small delay of the argument of the derivative and another delay which differs from a constant by a periodic perturbation of a small amplitude is considered. If the corresponding system with constant delay has an isolated ω-periodic solution and the period of the delay is not rationally dependent on ω, then under a nondegeneracy assumption it is proved that in any sufficiently small neighbourhood of this orbit the perturbed system has a unique almost periodic solution.
LA - eng
KW - 34A37; 34K10
UR - http://eudml.org/doc/268878
ER -

References

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  9. [9] A.A. Boichuk and V.C. Covachev: “Periodic solutions of impulsive systems with a small delay in the critical case of first order”, In: H. Akça, L. Berezansky, E. Braverman, L. Byszewski, S. Elaydi, I. Győri (Eds.): Functional Differential-Difference Equations and Applications, Antalya, Turkey, 18–23 August 1997, Electronic Publishing House. 
  10. [10] A.A. Boichuk and V.C. Covachev: “Periodic solutions of impulsive systems with a small delay in the critical case of second order”, Nonlinear Oscillations, No. 1, (1998), pp. 6–19. Zbl0949.34065
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  14. [14] V. Lakshmikantham, D.D. Bainov, P.S. Simeonov: “Theory of Impulsive Differential Equations”, Series in Modern Applied Mathematics 6, World Scientific, Singapore, 1989. Zbl0719.34002
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