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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  1. [1] H. Akça and V.C. Covachev: “Periodic solutions of impulsive systems with periodic delays”, In: H. Akça, V.C. Covachev, E. Litsyn (Eds.): Proceedings of the International Conference on Biomathematics Bioinformatics and Application of Functional Differential Difference Equations, Alanya, Turkey, 14–19 July, 1999, Publication of the Biology Department, Faculty of Arts and Sciences, Akdeniz University, Antalya, 1999, pp. 65–76. 
  2. [2] H. Akça and V.C. Covachev: “Periodic solutions of linear impulsive systems with periodic delays in the critical case”, In: Third International Conference on Dynamic Systems & Applications, Atlanta, Georgia, May 1999, Proceedings of Dynamic Systems and Applications, Vol. III, pp. 15–22. Zbl1003.34073
  3. [3] N.V. Azbelev, V.P. Maximov, L.F. Rakhmatullina: Introduction to the Theory of Functional Differential Equations, Nauka, Moscow, 1991. 
  4. [4] D.D. Bainov and V.C. Covachev: “Impulsive Differential Equations with a Small Parameter”, Series on Advances in Mathematics for Applied Sciences 24, World Scientific, Singapore, 1994. Zbl0828.34001
  5. [5] D.D. Bainov and V.C. Covachev: “Periodic solutions of impulsive systems with a small delay”, J. Phys. A: Math. and Gen., Vol. 27, (1994), pp. 5551–5563. http://dx.doi.org/10.1088/0305-4470/27/16/020 Zbl0837.34069
  6. [6] D.D. Bainov and V.C. Covachev: “Existence of periodic solutions of neutral impulsive systems with a small delay”, In: M. Marinov and D. Ivanchev (Eds.): 20th Summer School “Applications of Mathematics in Engineering”, Varna, 26.08-02.09, 1994, Sofia, 1995, pp. 35–40. Zbl0837.34069
  7. [7] D.D. Bainov and V.C. Covachev: “Periodic solutions of impulsive systems with delay viewed as small parameter”, Riv. Mat. Pura Appl., Vol. 19, (1996), pp. 9–25. Zbl0911.34010
  8. [8] D.D. Bainov, V.C. Covachev, I. Stamova: “Stability under persistent disturbances of impulsive differential-difference equations of neutral type”, J. Math. Anal. Appl., Vol. 187, (1994), pp. 799–808. http://dx.doi.org/10.1006/jmaa.1994.1390 Zbl0811.34057
  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
  11. [11] V.C. Covachev: “Almost periodic solutions of impulsive systems with periodic time-dependent perturbed delays”, Functional Differential Equations, Vol. 9, (2002), pp. 91–108. Zbl1091.34555
  12. [12] J. Hale: Theory of Functional Differential Equations, Springer, New York-Heidelberg-Berlin, 1977. Zbl0352.34001
  13. [13] L. Jódar, R.J. Villanueva, V.C. Covachev: “Periodic solutions of neutral impulsive systems with a small delay”, In: D.D. Bainov and V.C. Covachev (Eds.). Proceedings of the Fourth International Colloquium on Differential Equations, Plovdiv, Bulgaria, 18–22 August, 1993, VSP, Utrecht, The Netherlands, Tokyo, Japan, 1994, pp. 137–146. Zbl0843.34069
  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
  15. [15] A.M. Samoilenko and N.A. Perestyuk: “Impulsive Differential Equations”, World Scientific Series on Nonlinear Science. Ser. A: Monographs and Treatises 14, World Scientific, Singapore, 1995. Zbl0837.34003
  16. [16] D. Schley and S.A. Gourley: “Asymptotic linear stability for population models with periodic time-dependent perturbed delays”, In: Alcalá 1st International Conference on Mathematical Ecology, September 4–8, 1998, Alcalá de Henares, Spain, Abstracts, p. 146. Zbl0961.92026

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