Table of Contents Author Guidelines Submit a Manuscript
International Journal of Mathematics and Mathematical Sciences
Volume 2015, Article ID 828952, 17 pages
http://dx.doi.org/10.1155/2015/828952
Research Article

Periodic Solutions of Certain Differential Equations with Piecewise Constant Argument

Department of Mathematics, SUNY College at Buffalo, 1300 Elmwood Avenue, Buffalo, NY 14222-1095, USA

Received 30 March 2015; Accepted 27 May 2015

Academic Editor: Harvinder S. Sidhu

Copyright © 2015 James Guyker. 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. M. Shah and J. Wiener, “Advanced differential equations with piecewise constant argument deviations,” International Journal of Mathematics and Mathematical Sciences, vol. 6, no. 4, pp. 671–703, 1983. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. K. L. Cooke and J. Wiener, “Retarded differential equations with piecewise constant delays,” Journal of Mathematical Analysis and Applications, vol. 99, no. 1, pp. 265–297, 1984. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. A. R. Aftabizadeh, J. Wiener, and J.-M. Xu, “Oscillatory and periodic solutions of delay differential equations with piecewise constant argument,” Proceedings of the American Mathematical Society, vol. 99, no. 4, pp. 673–679, 1987. View at Publisher · View at Google Scholar · View at MathSciNet
  4. A. Cabada and J. B. Ferreiro, “First order differential equations with piecewise constant arguments and nonlinear boundary value conditions,” Journal of Mathematical Analysis and Applications, vol. 380, no. 1, pp. 124–136, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. J. Hong, R. Obaya, and A. Sanz, “Almost periodic type solutions of some differential equations with piecewise constant argument,” Nonlinear Analysis: Theory, Methods & Applications, vol. 45, no. 6, pp. 661–688, 2001. View at Publisher · View at Google Scholar · View at Scopus
  6. G. Wang, “Existence theorem of periodic solutions for a delay nonlinear differential equation with piecewise constant arguments,” Journal of Mathematical Analysis and Applications, vol. 298, no. 1, pp. 298–307, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. R. Yuan, “The existence of almost periodic solutions of retarded differential equations with piecewise constant argument,” Nonlinear Analysis: Theory, Methods & Applications, vol. 48, no. 7, pp. 1013–1032, 2002. View at Publisher · View at Google Scholar · View at Scopus
  8. Z. Zhou, “Periodic orbits on discrete dynamical systems,” Computers & Mathematics with Applications, vol. 45, no. 6–9, pp. 1155–1161, 2003. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. Y. Chen, “All solutions of a class of difference equations are truncated periodic,” Applied Mathematics Letters, vol. 15, no. 8, pp. 975–979, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  10. C. Hou and S. S. Cheng, “Eventually periodic solutions for difference equations with periodic coefficients and nonlinear control functions,” Discrete Dynamics in Nature and Society, vol. 2008, Article ID 179589, 21 pages, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. T. Yi and Z. Zhou, “Periodic solutions of difference equations,” Journal of Mathematical Analysis and Applications, vol. 286, no. 1, pp. 220–229, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  12. H. Zhu, L. Huang, and X. Liao, “Convergence and periodicity of solutions for a class of delay difference equations,” Computers and Mathematics with Applications, vol. 48, no. 10-11, pp. 1477–1484, 2004. View at Publisher · View at Google Scholar · View at Scopus
  13. S. Al-Ashhab and J. Guyker, “Piecewise defined recursive sequences with application in matrix theory,” Journal of Mathematical and Computational Science, vol. 2, no. 4, pp. 793–809, 2012. View at Google Scholar · View at MathSciNet