Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2014, Article ID 784289, 4 pages
http://dx.doi.org/10.1155/2014/784289
Research Article

Uniform Exponential Stability of Discrete Evolution Families on Space of -Periodic Sequences

1School of Informatics, Linyi University, Linyi, Shandong 276005, China
2Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan
3Laboratoire SAMM EA4543, Université Paris 1 Panthéon-Sorbonne, Centre P. M. F., 90 Rue de Tolbiac, 75634 Paris Cedex 13, France

Received 28 April 2014; Revised 30 June 2014; Accepted 1 July 2014; Published 31 August 2014

Academic Editor: Qi-Ru Wang

Copyright © 2014 Yongfang Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. C. Chicone and Y. Latushkin, Evolution Semigroups in Dynamical Systems and Differential Equations, vol. 70 of Mathematical Surveys and Monographs, American Mathematical Society, Providence, RI, USA, 1999. View at Publisher · View at Google Scholar · View at MathSciNet
  2. S. Clark, Y. Latushkin, S. Montgomery-Smith, and T. Randolph, “Stability radius and internal versus external stability in Banach spaces: an evolution semigroup approach,” SIAM Journal on Control and Optimization, vol. 38, no. 6, pp. 1757–1793, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  3. C. Buşe, S. S. Dragomir, and V. Lupulescu, “Characterizations of stability for strongly continuous semigroups by boundedness of its convolutions with almost periodic functions,” International Journal of Differential Equations and Applications, vol. 2, no. 1, pp. 103–109, 2001. View at Google Scholar · View at MathSciNet
  4. C. Buşe and V. Lupulescu, “Exponential stability of linear and almost periodic systems on Banach spaces,” Electronic Journal of Differential Equations, vol. 2003, pp. 1–7, 2003. View at Google Scholar · View at MathSciNet
  5. A. Zada, N. Ahmad, I. Khan, and F. Khan, “On the exponential stability of discrete semigroup,” Qualitative Theory of Dynamical Systems. In press.
  6. A. Khan, G. Rahmat, and A. Zada, “On uniform exponential stability and exact admissibility of discrete semigroups,” International Journal of Differential Equations, vol. 2013, 4 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  7. C. Buşe, A. Khan, G. Rahmat, and A. Tabassum, “Uniform exponential stability for nonautonomous system via discrete evolution semigroups,” Bulletin Mathématique de la Société des Sciences Mathématiques de Roumanie, vol. 57, pp. 193–205, 2014. View at Google Scholar
  8. C. Buşe and O. Jitianu, “A new theorem on exponential stability of periodic evolution families on Banach spaces,” Electronic Journal of Differential Equations, vol. 2003, pp. 1–10, 2003. View at Google Scholar · View at MathSciNet
  9. C. Buşe and A. Zada, “Dichotomy and boundedness of solutions for some discrete Cauchy problems,” in Topics in Operator Theory: Proceedings of IWOTA—2008, vol. 203 of Operator Theory: Advances and Applications, pp. 165–174, Birkhäuser, Basel, Switzerland, 2010. View at Publisher · View at Google Scholar
  10. A. Zada, “A characterization of dichotomy in terms of boundedness of solutions for some Cauchy problems,” Electronic Journal of Differential Equations, vol. 2008, pp. 1–5, 2008. View at Google Scholar · View at Scopus