Abstract and Applied Analysis

ψ -Exponential Stability of Nonlinear Impulsive Dynamic Equations on Time Scales

Veysel Fuat Hatipoğlu, Deniz Uçar, and Zeynep Fidan Koçak

Full-text: Open access

Abstract

The purpose of this paper is to present the sufficient ψ -exponential, uniform exponential, and global exponential stability conditions for nonlinear impulsive dynamic systems on time scales.

Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 103894, 5 pages.

Dates
First available in Project Euclid: 27 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393511838

Digital Object Identifier
doi:10.1155/2013/103894

Mathematical Reviews number (MathSciNet)
MR3044986

Zentralblatt MATH identifier
1276.34081

Citation

Hatipoğlu, Veysel Fuat; Uçar, Deniz; Koçak, Zeynep Fidan. $\psi $ -Exponential Stability of Nonlinear Impulsive Dynamic Equations on Time Scales. Abstr. Appl. Anal. 2013 (2013), Article ID 103894, 5 pages. doi:10.1155/2013/103894. https://projecteuclid.org/euclid.aaa/1393511838


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References

  • V. Lakshmikantham, D. D. Baĭnov, and P. S. Simeonov, Theory of Impulsive Differential Equations, vol. 6 of Series in Modern Applied Mathematics, World Scientific Publishing, Teaneck, NJ, USA, 1989.
  • D. D. Baĭnov and P. S. Simeonov, Systems with Impulse Effect: Stability, Theory and Applications, Ellis Horwood Series: Mathematics and its Applications, Ellis Horwood, Chichester, UK, 1989.
  • B. Gupta and S. K. Srivastava, “$\psi $-exponential stability for non-linear impulsive differential equations,” International Journal of Computational and Mathematical Sciences, vol. 4, no. 7, pp. 329–333, 2010.
  • J. Hoffacker and C. C. Tisdell, “Stability and instability for dynamic equations on time scales,” Computers & Mathematics with Applications, vol. 49, no. 9-10, pp. 1327–1334, 2005.
  • J. J. DaCunha, “Stability for time varying linear dynamic systems on time scales,” Journal of Computational and Applied Mathematics, vol. 176, no. 2, pp. 381–410, 2005.
  • A. C. Peterson and C. C. Tisdell, “Boundedness and uniqueness of solutions to dynamic equations on time scales,” Journal of Difference Equations and Applications, vol. 10, no. 13–15, pp. 1295–1306, 2004.
  • A. C. Peterson and Y. N. Raffoul, “Exponential stability of dynamic equations on time scales,” Advances in Difference Equations, vol. 2005, Article ID 858671, 2005.
  • A.-L. Liu, “Boundedness and exponential stability of solutions to dynamic equations on time scales,” Electronic Journal of Differential Equations, vol. 2007, article 12, 14 pages, 2007.
  • S. K. Choi, N. J. Koo, and D. M. Im, “$h$-stability for linear dynamic equations on time scales,” Journal of Mathematical Analysis and Applications, vol. 324, no. 1, pp. 707–720, 2006.
  • M. Benchohra, J. Henderson, and S. Ntouyas, Impulsive Differential Equations and Inclusions, vol. 2 of Contemporary Mathematics and Its Applications, Hindawi Publishing Corporation, New York, NY, USA, 1st edition, 2006.
  • M. Benchohra, J. Henderson, S. K. Ntouyas, and A. Ouahab, “On first order impulsive dynamic equations on time scales,” Journal of Difference Equations and Applications, vol. 10, no. 6, pp. 541–548, 2004.
  • V. Lakshmikantham and A. S. Vatsala, “Hybrid systems on time scales,” Journal of Computational and Applied Mathematics, vol. 141, no. 1-2, pp. 227–235, 2002.
  • V. Lupulescu and A. Zada, “Linear impulsive dynamic systems on time scales,” Electronic Journal of Qualitative Theory of Differential Equations, no. 11, pp. 1–30, 2010.
  • E. R. Kaufmann, N. Kosmatov, and Y. N. Raffoul, “Impulsive dynamic equations on a time scale,” Electronic Journal of Differential Equations, vol. 2008, article 67, 9 pages, 2008.
  • Y. Ma and J. Sun, “Stability criteria for impulsive systems on time scales,” Journal of Computational and Applied Mathematics, vol. 213, no. 2, pp. 400–407, 2008.
  • \.I. B. Yaşar and A. Tuna, “$\psi $-uniformly stability for time varying linear dynamic systems on time scales,” International Mathematical Forum, vol. 2, no. 17–20, pp. 963–972, 2007.
  • M. Bohner and A. Peterson, Dynamic Equations on Time Scales, An Introduction with Applications, Birkhäuser, Boston, Mass, USA, 2001.