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International Journal of Differential Equations
Volume 2015 (2015), Article ID 618359, 11 pages
http://dx.doi.org/10.1155/2015/618359
Research Article

A Stability Result for the Solutions of a Certain System of Fourth-Order Delay Differential Equation

1Department of Mathematics, Faculty of Science, Assiut University, Assiut 71516, Egypt
2Department of Mathematics, Faculty of Science, Assiut University, New Valley Branch, New Valley, El-khargah 72111, Egypt

Received 25 September 2014; Revised 11 February 2015; Accepted 13 February 2015

Academic Editor: Davood D. Ganji

Copyright © 2015 A. M. A. Abou-El-Ela 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. A. M. Lyapunov, Stability of Motion, Academic Press, New York, NY, USA, 1966. View at MathSciNet
  2. N. N. Krasovskii, “On conditions of inversion of A. M. Lyapunov's theorems on instability for stationary systems of differential equations,” Doklady Akademii Nauk SSSR (N.S.), vol. 101, pp. 17–20, 1955 (Russian). View at Google Scholar · View at MathSciNet
  3. T. Yoshizawa, Stability Theory by Lyapunov's Second Method, The Mathematical Society of Japan, 1966. View at MathSciNet
  4. R. Reissig, G. Sansone, and R. Conti, Nonlinear Differential Equations of Higher-Order, Noordhoff International Publishing, Leyden, The Netherlands, 1974, translated from the German.
  5. A. M. Abou-El-Ela and A. I. Sadek, “A stability result for the solutions of a certain system of fourth-order differential equations,” Annals of Differential Equations, vol. 6, no. 2, pp. 131–141, 1990. View at Google Scholar · View at MathSciNet
  6. A. M. A. Abou-El-Ela and A. I. Sadek, “A stability theorem for a certain fourth-order vector differential equation,” Annals of Differential Equations, vol. 10, no. 2, pp. 125–134, 1994. View at Google Scholar · View at MathSciNet
  7. A. M. A. Abou-El-Ela and A. I. Sadek, “On the asymptotic behaviour of solutions of certain non-autonomous differential equations,” Journal of Mathematical Analysis and Applications, vol. 237, no. 1, pp. 360–375, 1999. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. H. Bereketoglu and C. Kart, “Some results for a certain third-order nonlinear ordinary differential equation,” Bulletin Mathématique de la Société des Sciences Mathématiques de Roumanie, vol. 39, no. 1–4, pp. 77–83, 1996. View at Google Scholar
  9. A. I. Sadek, “On the stability of solutions of certain fourth-order delay differential equations,” Applied Mathematics and Computation, vol. 148, no. 2, pp. 587–597, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. C. Tunç, “Some stability results for the solutions of certain fourthorder delay differential equations,” Journal of Difference Equations and Applications, vol. 4, pp. 165–174, 2005. View at Google Scholar
  11. C. Tunç, “On stability of solutions of certain fourth-order delay differential equations,” Applied Mathematics and Mechanics. English Edition, vol. 27, no. 8, pp. 1141–1148, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. C. Tunç, “On asymptotic stability of solutions to third-order nonlinear differential equations with retarded argument,” Communications in Applied Analysis, vol. 11, no. 3-4, pp. 515–527, 2007. View at Google Scholar · View at MathSciNet
  13. C. Tunç, “On the stability of solutions to a certain fourth-order delay differential equation,” Nonlinear Dynamics, vol. 51, no. 1-2, pp. 71–81, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. A. M. A. Abou-El-Ela, A. I. Sadek, and A. M. Mahmoud, “On the stability of solutions to a certain fourth-order vector delay differential equation,” Annals of Differential Equations, vol. 28, no. 1, pp. 1–10, 2012. View at Google Scholar · View at MathSciNet
  15. T. A. Burton, Stability and Periodic Solutions of Ordinary and Functional Differential Equations, Academic Press, New York, NY, USA, 1985. View at MathSciNet
  16. R. Bellman, Introduction to Matrix Analysis, Classics in Applied Mathematics 19, reprint of the second edition (1970), with a foreword by Gene Golub, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, Pa, USA, 1997.