ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

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Existence and Uniqueness of Periodic Solutions for a Kind of Third-order Functional Differential Equation with a Time-delay

Автор(ы):

A. M. Mahmoud

Department of Mathematics, Faculty of Science,
New Valley Branch,
Assiut University. New Valley,
El-Khargah 72111, Egypt

math_ayman27@yahoo.com

Аннотация:

In this paper, by using the Mawhin coincidence degree theory and analysis techniques, we establish new results on the existence and uniqueness of T-periodic solutions for a kind of third-order functional differential equation (FDE) with a time-delay. The obtained results are new and complement the related results of third-order (FDE) with a time-delay that have appeared in the literature. In the last section, we give an example to illustrate our main results of periodic solutions.

Ключевые слова

Ссылки:

  1. A. M. A. Abou-El-Ela, A. I. Sadek and A. M. Mahmoud, Periodic solutions for a kind of third-order delay differential equations with a deviating argument, J. Math. Sci. Univ. Tokyo}, 18, 35-49, 2011
  2. A. M. A. Abou-El-Ela, A. I. Sadek and A. M. Mahmoud, Existence and uniqueness of a periodic solution for third-order delay differential equation with two deviating arguments, IAENG International Journal of Applied Mathematics, 42(1), 7-12, 2012
  3. T. A. Burton, Stability and Periodic Solutions of Ordinary and Functional Differential Equations, Academic Press, 1985
  4. R. E. Gaines and J. Mawhin, Coincidence Degree and Nonlinear Differential Equations, Lecture Notes in Math., Springer-Verlag, Berlin, 568, 1977
  5. Z. Gui, Existence of positive periodic solutions to third-order delay differential equations, Electron. J. Differential Equations, 91, 1-7, 2006
  6. S. A. Iyase and O. J. Adeleke, On the existence and uniqueness of periodic solution for a third-order neutral functional differential equation, Int. J. Math. Anal., 10(17), 817-831, 2016
  7. V. Kolmanovskii and A. Myshkis, Introduction to the theory and applications of functional differential equations, Kluwer Academic Publishers, Dordrecht, 1999
  8. Y. Kuang, Delay Differential Equations with Applications in Population Dynamical system, Academic Press, New York, 1993
  9. B. Liu, L. Huang and Y. Li, Existence of periodic solutions of a third-order functional differential equation, Acta Math. Appl. Sin., 29(2), 226-233, 2006
  10. H. P. Long and X. H. Hou, Existence of periodic solutions of a third-order functional differential equation, Math. Theory Appl., 28(1), 82-85, 2008
  11. G. Makay, Periodic solutions of linear functional differential and integral equations, Differential Integral Equations, 8(8), 2177-2187, 1995
  12. G. Makay, Periodic solutions of dissipative functional differential equations with infinite delay, Tohoku Math. J., 48, 355-362, 1996
  13. H. O. Tejumola and B. Tchegnani, Stability, boundedness and existence of periodic solutions of some third and fourth-order nonlinear delay differential equations, J. Nigerian Math. Soc., 19, 9-19, 2000
  14. C. Tunc, On existence of periodic solution to certain nonlinear third-order differential equations, Proyecciones, 28(2), 125-132, 2009
  15. C. Tunc, On the existence of periodic solutions to nonlinear third-order ordinary differential equations with delay, J. Comput. Anal. Appl., 12(1-B), 191-201, 2010
  16. C. Tunc, Existence of periodic solutions to nonlinear differential equations of third-order with multiple deviating arguments, International Journal of Differential Equations, 2012, 1-13, 2012
  17. C. Tunc, On existence of periodic solutions of functional differential equations of the third-order, Appl. Comput. Math. }, 15(2), 189-199, 2016
  18. Z. Zhang and Z. Wang, Periodic solutions of third-order functional differential equations with variable coefficients, Appl. Math. J. Chinese Univ. Ser. B, 17(2), 145-154, 2002
  19. Z. Zhang and Z. Wang, Periodic solutions of the third-order functional differential equations, J. Math. Anal. Appl., 292(1), 115-134, 2004
  20. Z. Zhang, Z. Wang and J. Yu, On the existence of periodic solutions of third-order functional differential equations, Funkcial. Ekvac., 43(3), 461-469, 2000
  21. Y. Zhu, On stability, boundedness and existence of periodic solution of a kind of third-order nonlinear delay differential system, Ann. Differential Equations, 8(2), 249-259, 1992

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