The main purpose of this paper is to investigate global asymptotic
stability of the zero solution of the fifth-order nonlinear delay differential
equation on the following form
By constructing a Lyapunov functional, sufficient conditions for the
stability of the zero solution of this equation are established.
Cite this paper
Abou-El-Ela, A. , Sadek, A. , Mahmoud, A. and Taie, R. (2014) On the Stability of Solutions of Nonlinear Functional Differential Equation of the Fifth-Order. Advances in Pure Mathematics
, 357-367. doi: 10.4236/apm.2014.48046
 Adesina, O.A. (2007) Convergence Results for Solutions of a Certain Fifth-Order Nonlinear Differential Equation. Nonlinear Studies, 14, 289-300.
 Bereketoglu, H. (1998) Asymptotic Stability of a Fourth-Order Delay Differential Equation. Dynamic Systems an Applications, 7, 105-115.
 Burton, T.A. (1983) Volterra Integral and Differential Equations. Academic Press, New York.
 Burton, T.A. (1985) Stability and Periodic Solutions of Ordinary and Functional Differential Equations. Academic Press, New York.
 Chukwu, E.N. (1978) On the Boundedness and the Existence of a Periodic Solution of Some Nonlinear Third-Order Delay Differential Equation. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat., 64, 440-447.
 Harrow, M. (1967) A Stability Result for Solutions of Certain Fourth-Order Homogeneous Differential Equations. Journal London Mathematical Society, 42, 51-56. http://dx.doi.org/10.1112/jlms/s1-42.1.51
 Harrow, M. (1970) On the Boundedness and the Stability of Solutions of Some Differential Equations of the Fourth-Order. SIAM Journal on Mathematical Analysis, 1, 27-32. http://dx.doi.org/10.1137/0501002
 Hale, J.K. (1977) Theory of Functional Differential Equations. Springer-Verlag, New York. http://dx.doi.org/10.1007/978-1-4612-9892-2
 Kolmanovskii, V. and Myshkis, A. (1999) Introduction to the Theory and Applications of Functional Differential Equations. Kluwer Academic Publishers, Dordrecht. http://dx.doi.org/10.1007/978-94-017-1965-0
 Makay, G. (1994) On the Asymptotic Stability of the Solutions of Functional Differential Equations with Infinite Delay. Journal of Differential Equations, 108, 139-151. http://dx.doi.org/10.1006/jdeq.1994.1029
 Okoronkwo, E.O. (1989) On Stability and Boundedness of Solutions of a Certain Fourth-Order Delay Differential Equation. International Journal of Mathematics and Mathematical Sciences, 12, 589-602. http://dx.doi.org/10.1155/S0161171289000724
 Reissing, R., Sansone, E. and Conti, R. (1974) Non-Linear Differential Equations of Higher-Order. Noordhoof, Toom.
 Sadek, A.I. (2003) Stability and Boundedness of a Kind of Third-Order Delay Differential System. Applied Mathematics Letters, 16, 657-662. http://dx.doi.org/10.1016/S0893-9659(03)00063-6
 Sadek, A.I. (2004) On the Stability of Solutions of Certain Fourth-Order Delay Differential Equations. Applied Mathe-matics and Computation, 148, 587-597. http://dx.doi.org/10.1016/S0096-3003(02)00925-6
 Sadek, A.I. (2005) On the Stability of Solutions of Some Non-Autonomous Delay Differential Equations of the Third-Order. Asymptotic Analysis, 43, 1-7.
 Li, S.L. and Wen, L.Z. (1987) Functional Differential Equations. Hunan Science and Technology Press, Changsha.
 Sinha, A.S.C. (1973) On Stability of Solutions of Some Third and Fourth-Order Delay Differential Equations. Information and Control, 23, 165-172. http://dx.doi.org/10.1016/S0019-9958(73)90651-7
 Tejumola, H.O. and Tchegnani, B. (2000) Stability, Boundedness and Existence of Periodic Solutions of Some Third and Fourth-Order Nonlinear Delay Differential Equations. Journal of the Nigerian Mathematics Society, 19, 9-19.
 Tunc, C. (2002) A Study of the Stability and Boundedness of the Solutions of Nonlinear Differential Equations of the Fifth-Order. Indian Journal of Pure and Applied Mathematics, 33, 519-529.
 Tunc, C. (2005) Some Stability Results for the Solutions of Certain Fourth-Order Delay Differential Equations. Differential Equations & Applications, 4, 165-174.
 Tunc, C. (2006) On the Stability of Solutions of Certain Fourth-Order Delay Differential Equations. Applied Mathematics and Mechanics, 27, 1141-1148.
 Tunc, C. (2008) On the Stability of Solutions to a Certain Fourth-Order Delay Differential Equation. Nonlinear Dynamics, 51, 71-81. http://dx.doi.org/10.1007/s11071-006-9192-z
 Tunc, C. (2010) On Asymptotic Stability of Solutions of Fifth-Order Nonlinear Differential Equations with Delay. Functional Differential Equations, 17, 355-370.
 Tunc, C. (2013) New Results on the Stability and Boundedness of Nonlinear Differential Equations of Fifth-Order with Multiple Deviating Arguments. Bulletin of the Malaysian Mathematical Sciences Society, 36, 671-682.
 Yoshizawa, T. (1966) Stability Theory by Lyapunov’s Second Method. The Mathematical Society of Japan.
 Qin, Y., Liu, Y. and Wang, L. (1966) Stability of Motion for Dynamic Systems with Delay. Academic Press, Beijing.
 Zhu, Y. (1992) On Stability, Boundedness and Existence of Periodic Solution of a Kind of Third-Order Nonlinear Delay Differential System. Annals of Differential Equations, 8, 249-259.
 Lyapunov, A.M. (1966) Stability of Motion. Academic Press, London.
 Tunc, C. (2010) On the Stability of Solutions of Nonlinear Differential Equations of Fifth-Order with Delay. Mathematical Communications, 15, 261-272.
 Abou-El-Ela, A.M.A., Sadek, A.I. and Mahmoud, A.M. (2011) On the Stability of Solutions of a Certain Nonlinear Delay Differential Equation of the Fifth-Order. Proceedings of the 3rd Scientific Conference for Young Researchers, Assiut, 19-20 April 2011.
 Burton, T.A. and Hering, G. (1994) Lyapunov Theory for Functional Differential Equations. Rocky Mountain Journal of Mathematics, 24, 3-17. http://dx.doi.org/10.1216/rmjm/1181072449
 Hale, J.K. (1965) Sufficient Conditions for Stability and Instability of Autonomous Functional-Differential Equations. Journal of Differential Equations, 1, 452-482. http://dx.doi.org/10.1016/0022-0396(65)90005-7