About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 707319, 17 pages
http://dx.doi.org/10.1155/2012/707319
Research Article

Periodic Solutions in Shifts 𝜹 ± for a Nonlinear Dynamic Equation on Time Scales

Department of Mathematics, Ege University, Bornova, 35100 Izmir, Turkey

Received 16 March 2012; Accepted 27 June 2012

Academic Editor: Elena Braverman

Copyright © 2012 Erbil Çetin and F. Serap Topal. 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. S. Hilger, Ein Masskettenkalkl mit Anwendug auf Zentrumsmanningfaltigkeiten [Ph.D. thesis], Universität Würzburg, 1988.
  2. E. R. Kaufmann and Y. N. Raffoul, “Periodic solutions for a neutral nonlinear dynamical equation on a time scale,” Journal of Mathematical Analysis and Applications, vol. 319, no. 1, pp. 315–325, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. X. L. Liu and W. T. Li, “Periodic solutions for dynamic equations on time scales,” Nonlinear Analysis, vol. 67, no. 5, pp. 1457–1463, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. M. Adıvar, “Function bounds for solutions of Volterra integro dynamic equations on the time scales,” Electronic Journal of Qualitative Theory of Differential Equations, no. 7, pp. 1–22, 2010.
  5. M. Adıvar and Y. N. Raffoul, “Existence of resolvent for Volterra integral equations on time scales,” Bulletin of the Australian Mathematical Society, vol. 82, no. 1, pp. 139–155, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. Y. N. Raffoul, “Periodic solutions for neutral nonlinear differential equations with functional delay,” Electronic Journal of Differential Equations, vol. 2003, no. 102, pp. 1–7, 2003. View at Zentralblatt MATH
  7. M. R. Maroun and Y. N. Raffoul, “Periodic solutions in nonlinear neutral difference equations with functional delay,” Journal of the Korean Mathematical Society, vol. 42, no. 2, pp. 255–268, 2005. View at Publisher · View at Google Scholar
  8. M. Adıvar and Y. N. Raffoul, “Shift operators and stability in delayed dynamic equations,” Rendiconti del Seminario Matematico, vol. 68, no. 4, pp. 369–396, 2011. View at Zentralblatt MATH
  9. M. Adıvar and Y. N. Raffoul, “Existence results for periodic solutions of integro-dynamic equations on time scales,” Annali di Matematica Pura ed Applicata IV, vol. 188, no. 4, pp. 543–559, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. M. Bohner and A. Peterson, Dynamic Equations on Time Scales, An Introduction with Applications, Birkhäuser, Boston, Mass, USA, 2001. View at Publisher · View at Google Scholar
  11. M. Bohner and A. Peterson, Eds., Advances in Dynamic Equations on Time Scales, Birkhäuser, Boston, Mass, USA, 2003. View at Publisher · View at Google Scholar
  12. M. Adıvar, “A new periodicity concept for time scales,” Mathematica Slovaca. In press.
  13. D. R. Smart, Fixed Point Theorems, Cambridge University Press, Cambridge, UK, 1980.