Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

On the Stability of Solutions for Non-autonomous Delay Differential Equations of Third-order

Author(s):

Lynda Oudjedi

Department of Mathematics.
University of Oran.
Algeria

oudjedi@yahoo.fr

Djamila Beldjerd

Department of Mathematics.
University of Oran.
Algeria

beldjerd2011@yahoo.com

Moussadek Remili

Department of Mathematics.
University of Oran.
Algeria

remilimous@gmail.com

Abstract:

In this paper we give sufficient conditions for the asymptotic stability and uniform boundedness for certain third order delay differential equation by constructing Lyapounov functionals. This result generalizes some asymptotic stability and uniform boundedness for certain third order delay differential equation.

References:

1. T. A. Burton, Stability and periodic solutions of ordinary and functional differential equations, Mathematics in Science and Engineering, 178. Academic Press, Inc., Orlando, FL, 1985
2. John. R. Graef and Moussadek. Remili, Some properties of monotonic solutions of x'''+p(t)x'+q(t)f(x)=0. Pan. American Mathematical journal V. 22(2012) no. 2, p. 31-39
3. M . O. Omeike, New results on the stability of solution of some non-autonomous delay differential equations of the third order, El. journal Differential Equations and Control Processes 2010 1, (2010), p. 18--29
4. M. O. Omeike, Stability and boundedness of solutions of some non-autonomous delay differential equation of the third order, An. Stiint. Univ. Al. I. Cuza Iasi. Mat. (N. S. ), 55(1), (2009), p. 49-58
5. A. I. Sadek, On the Stability of Solutions of Some Non-Autonomous Delay Differential Equations of the Third Order, Asymptot. Anal., 43 no. (1-2) (2005), p. 1-–7
6. A. I. Sadek, Stability and Boundedness of a Kind of Third-Order Delay Differential System, Applied Mathematics Letters, 16(5) (2003), p. 657-–662
7. C. Tunc, On asymptotic stability of solutions to third order nonlinear differential equations with retarded argument, Communications in Applied Analysis, 11 (2007), no (4), p. 515--528
8. C. Tunc, On the asymptotic behavior of solutions of certain third-order nonlinear differential equations, J. Appl. Math. Stoch. Anal. 1(2005), 29{35}
9. C. Tunc, On the stability and boundedness of solutions to third order nonlinear differential equations with retarded argument, Nonlinear Dynam. 57 (2009), no. 1-2, 97-106. EJQTDE, 2010 No. 12, p. 18
10. C. Tunc, Some stability and boundedness conditions for non-autonomous differential equations with deviating arguments, E. J. Qualitative Theory of Diff. Equ., No. 1. (2010), p. 1--12
11. C. Tunc, Stability and boundedness of solutions of nonlinear differential equations of third-order with delay, El. Journal Differential Equations and Control Processes (Differentsial'nye Uravneniya i Protsessy Upravleniya), No. 3, 2007, p. 1-13
12. T. Yoshizawa, Stability theory by Liapunov's second method, The Mathematical Society of Japan, Tokyo, 1966
13. Y. F. Zhu, On stability, boundedness and existence of periodic solution of a kind of third order nonlinear delay differential system, Ann. Differential Equations 8 (2) (1992), p. 249--259

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