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

• Autorzy: Valéry Covachev , Zlatinka Covacheva , Haydar Akça , Eada Al-Zahrani
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

neutral impulsive system; almost periodic solution; 34A37; 34K10

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2003
• Tom: 1
• Numer: 3
• Strony: 292-314

Daty

wydano

2003-09-01

online

2003-09-01

Twórcy

autor

Valéry Covachev

• Bulgarian Academy of Sciences

autor

Zlatinka Covacheva

• Higher College of Telecommunications and Post

autor

Haydar Akça

• King Fahd University of Petroleum and Minerals

autor

Eada Al-Zahrani

• Sciences College for Girls

Bibliografia

• [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] 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.
• [3] N.V. Azbelev, V.P. Maximov, L.F. Rakhmatullina: Introduction to the Theory of Functional Differential Equations, Nauka, Moscow, 1991.
• [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.
• [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
• [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.
• [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.
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• [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] 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.
• [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.
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• [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.
• [14] V. Lakshmikantham, D.D. Bainov, P.S. Simeonov: “Theory of Impulsive Differential Equations”, Series in Modern Applied Mathematics 6, World Scientific, Singapore, 1989.
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Identyfikatory

DOI

10.2478/BF02475211