Table of Contents Author Guidelines Submit a Manuscript
International Journal of Differential Equations
Volume 2015 (2015), Article ID 213935, 12 pages
http://dx.doi.org/10.1155/2015/213935
Research Article

Stability, Boundedness, and Existence of Periodic Solutions to Certain Third-Order Delay Differential Equations with Multiple Deviating Arguments

Research Group in Differential Equations and Applications (RGDEA), Department of Mathematics, Obafemi Awolowo University, Ile-Ife 220005, Nigeria

Received 13 July 2015; Accepted 31 August 2015

Academic Editor: Nikolai N. Leonenko

Copyright © 2015 A. T. Ademola 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. T. A. Burton, “Stability and periodic solutions of ordinary and functional differential equations,” in Mathematics in Science and Engineering, vol. 178, Academic Press, Orlando, Fla, USA, 1985. View at Google Scholar
  2. T. A. Burton, Volterra Integral and Differential Equations, Academic Press, New York, NY, USA, 1983.
  3. R. D. Driver, Ordinary and Delay Differential Equations, Springer, New York, NY, USA, 1976.
  4. J. K. Hale, Theory of Functional Differential Equations, Springer, New York, NY, USA, 1977.
  5. T. Yoshizawa, Stability Theory by Liapunov's Second Method, The Mathematical Society of Japan, 1966.
  6. T. Yoshizawa, Stability Theory and Existence of Periodic Solutions and Almost Periodic Solutions, Springer, Berlin, Germany, 1975.
  7. A. M. A. Abou-El-Ela, A. I. Sadek, and A. M. Mahmoud, “Stability and boundedness of solutions of certain third order non linear delay differential equation,” ICGST-ACSE Journal, vol. 9, no. 1, pp. 9–15, 2009. View at Google Scholar
  8. A. T. Ademola and P. O. Arawomo, “Uniform stability and boundedness of solutions of nonlinear delay differential equations of the third order,” Mathematical Journal of Okayama University, vol. 55, pp. 157–166, 2013. View at Google Scholar
  9. A. T. Ademola, “Existence and uniqueness of a periodic solution to certain third order nonlinear delay differential equation with multiple deviating arguments,” Acta Universitatis Sapientiae, Mathematica, vol. 5, no. 2, pp. 113–131, 2013. View at Google Scholar
  10. A. T. Ademola, P. O. Arawomo, M. O. Ogunlaran, and E. A. Oyekan, “Uniform stability, boundedness and asymptotic behaviour of solutions of some third order nonlinear delay differential equations,” Differential Equations and Control Processes, no. 4, pp. 43–66, 2013. View at Google Scholar
  11. O. A. Adesina, “Results on the qualitative behaviour of solutions for a class of third order nonlinear differential equations,” AIP Conference Proceedings, vol. 1637, no. 1, pp. 5–12, 2014. View at Google Scholar
  12. A. U. Afuwape and M. O. Omeike, “Stability and boundedness of solutions of a kind of third-order delay differential equations,” Computational and Applied Mathematics, vol. 29, no. 3, pp. 329–342, 2010. View at Publisher · View at Google Scholar · View at Scopus
  13. E. N. Chukwu, “On the boundedness and the existence of a periodic solutions of some nonlinear third order delay differential equation,” Atti della Academia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, vol. 64, no. 5, pp. 440–447, 1978. View at Google Scholar
  14. Z. Gui, “Existence of positive periodic solutions to third order delay differential equations,” Electronic Journal of Differential Equations, vol. 91, pp. 1–7, 2006. View at Google Scholar
  15. M. O. Omeike, “New results on the stability of solution of some non-autonomous delay differential equations of the third-order,” Differential Equations and Control Processes, vol. 1, pp. 18–29, 2010. View at Google Scholar
  16. M. O. Omeike, “Uniform ultimate boundedness of solutions of third-order nonlinear delay differential equations,” Analele Ştiintifice ale Universităţii “Al.I.Cuza” din Iaşi, Matematica, vol. 56, no. 2, pp. 363–372, 2010. View at Google Scholar
  17. A. I. Sadek, “Stability and boundedness of a kind of third-order delay differential system,” Applied Mathematics Letters, vol. 16, no. 5, pp. 657–662, 2003. View at Publisher · View at Google Scholar · View at Scopus
  18. H. O. Tejumola and B. Tchegnani, “Stability, boundedness and existence of periodic solutions of some third order and fourth-order nonlinear delay differential equations,” Journal of the Nigerian Mathematical Society, vol. 19, pp. 9–19, 2000. View at Google Scholar
  19. C. Tunç and H. Ergören, “Uniformly boundedness of a class of non-linear differential equations of third order with multiple deviating arguments,” CUBO, vol. 14, no. 3, pp. 63–69, 2012. View at Google Scholar
  20. C. Tunç and M. Gözen, “Stability and uniform boundedness in multidelay functional differential equations of third order,” Abstract and Applied Analysis, vol. 2013, Article ID 248717, 7 pages, 2013. View at Publisher · View at Google Scholar
  21. C. Tunç, “A new result on the stability of solutions of a nonlinear differential equation of third order with finite lag,” Southeast Asian Bulletin of Mathematics, vol. 33, pp. 947–958, 2009. View at Google Scholar
  22. C. Tunç, “Existence of periodic solutions to nonlinear differential equations of third order with multiple deviating arguments,” International Journal of Differential Equations, vol. 2012, Article ID 406835, 13 pages, 2012. View at Publisher · View at Google Scholar · View at Scopus
  23. C. Tunç, “On existence of periodic solutions to nonlinear third order differential equations with delay,” Journal of Computational Analysis and Applications, vol. 12, no. 1, pp. 191–201, 2010. View at Google Scholar
  24. C. Tunç, “On the stability and boundedness of solutions of nonlinear third order differential equations with delay,” Filomat, vol. 24, no. 3, pp. 1–10, 2010. View at Publisher · View at Google Scholar · View at Scopus
  25. C. Tuņ, “On the qualitative behaviors of solutions to a kind of nonlinear third order differential equations with retarded argument,” Italian Journal of Pure and Applied Mathematics, no. 28, pp. 273–284, 2011. View at Google Scholar · View at Scopus
  26. C. Tunç, “Some stability and boundedness conditions for non-autonomous differential equations with deviating arguments,” Electronic Journal of Qualitative Theory of Differential Equations, no. 1, pp. 1–12, 2010. View at Google Scholar · View at Scopus
  27. C. Tunç, “Stability and boundedness for a kind of non-autonomous differential equations with constant delay,” Applied Mathematics and Information Sciences, vol. 7, no. 1, pp. 355–361, 2013. View at Publisher · View at Google Scholar · View at Scopus
  28. C. Tunç, “Stability and boundedness of solutions of nonlinear differential equations of third-order with delay,” Differential Equations and Control Processes, no. 3, pp. 1–13, 2007. View at Google Scholar
  29. H. Yao and J. Wang, “Globally asymptotic stability of a kind of third order delay differential system,” International Journal of Nonlinear Science, vol. 10, no. 1, pp. 82–87, 2010. View at Google Scholar
  30. Y. F. Zhu, “On stability, boundedness and existence of periodic solution of a kind of third order nonlinear delay differential system,” Annals of Differential Equations, vol. 8, no. 2, pp. 249–259, 1992. View at Google Scholar
  31. T. A. Ademola, M. O. Ogundiran, P. O. Arawomo, and O. A. Adesina, “Boundedness results for a certain third order nonlinear differential equation,” Applied Mathematics and Computation, vol. 216, no. 10, pp. 3044–3049, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus