Geodesic
Stability and Boundednessof the Solutions of Non Autonomous Third Order Differential Equations with Delay
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 53 (2014) no. 2, pp. 139-147 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

In this article, we shall establish sufficient conditions for the asymptotic stability and boundedness of solutions of a certain third order nonlinear non-autonomous delay differential equation, by using a Lyapunov function as basic tool. In doing so we extend some existing results. Examples are given to illustrate our results.
In this article, we shall establish sufficient conditions for the asymptotic stability and boundedness of solutions of a certain third order nonlinear non-autonomous delay differential equation, by using a Lyapunov function as basic tool. In doing so we extend some existing results. Examples are given to illustrate our results.
Classification : 34C11, 34D20
Keywords: Stability; Lyapunov functional; delay differential equations; third-order differential equations 
@article{AUPO_2014_53_2_a8,
     author = {Remili, Moussadek and Oudjedi, Lynda Damerdji},
     title = {Stability and {Boundednessof} the {Solutions} of {Non} {Autonomous} {Third} {Order} {Differential} {Equations} with {Delay}},
     journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
     pages = {139--147},
     year = {2014},
     volume = {53},
     number = {2},
     mrnumber = {3331011},
     zbl = {1317.34157},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AUPO_2014_53_2_a8/}
}
TY  - JOUR
AU  - Remili, Moussadek
AU  - Oudjedi, Lynda Damerdji
TI  - Stability and Boundednessof the Solutions of Non Autonomous Third Order Differential Equations with Delay
JO  - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY  - 2014
SP  - 139
EP  - 147
VL  - 53
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/AUPO_2014_53_2_a8/
LA  - en
ID  - AUPO_2014_53_2_a8
ER  - 
%0 Journal Article
%A Remili, Moussadek
%A Oudjedi, Lynda Damerdji
%T Stability and Boundednessof the Solutions of Non Autonomous Third Order Differential Equations with Delay
%J Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
%D 2014
%P 139-147
%V 53
%N 2
%U http://geodesic.mathdoc.fr/item/AUPO_2014_53_2_a8/
%G en
%F AUPO_2014_53_2_a8
Remili, Moussadek; Oudjedi, Lynda Damerdji. Stability and Boundednessof the Solutions of Non Autonomous Third Order Differential Equations with Delay. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 53 (2014) no. 2, pp. 139-147. http://geodesic.mathdoc.fr/item/AUPO_2014_53_2_a8/

[1] Burton, T. A.: Stability and periodic solutions of ordinary and functional differential equations. Mathematics in Science and Engineering 178, Academic Press, Orlando, FL, 1985. | MR | Zbl

[2] Burton, T. A., Makay, G.: Asymptotic stability for functional differential equations. Acta Math. Hung. 65, 3 (1994), 243–251. | DOI | MR | Zbl

[3] Greaf, J. R., Remili, M.: Some properties of monotonic solutions of $x^{\prime \prime \prime }+p(t)x^{\prime }+q(t)f(x)=0$. Pan. American Math. J. 22, 2 (2012), 31–39. | MR

[4] Omeike, M. O.: New results on the stability of solution of some non-autonomous delay differential equations of the third order. Differential Equations and Control Processes 2010, 1 (2010), 18–29. | MR

[5] Omeike, M. O.: 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), 49–58. | MR | Zbl

[6] Sadek, A. I.: On the Stability of Solutions of Some Non-Autonomous Delay Differential Equations of the Third Order. Asymptot. Anal. 43, 1-2 (2005), 1–7. | MR | Zbl

[7] Sadek, A. I.: Stability and Boundedness of a Kind of Third-Order Delay Differential System. Applied Mathematics Letters 16, 5 (2003), 657–662. | DOI | MR | Zbl

[8] Swick, K.: On the boundedness and the stability of solutions of some non- autonomous differential equations of the third order. J. London Math. Soc. 44 (1969), 347–359. | DOI | MR | Zbl

[9] Tunç, C.: On asymptotic stability of solutions to third order nonlinear differential equations with retarded argument. Communications in applied analysis 11, 4 (2007), 515–528. | MR | Zbl

[10] Tunç, C.: On the asymptotic behavior of solutions of certain third-order nonlinear differential equations. J. Appl. Math. Stoch. Anal. 2005, 1 (2005), 29–35. | DOI | Zbl

[11] Tunç, C.: On the stability and boundedness of solutions to third order nonlinear differential equations with retarded argument. Nonlinear Dynamics 57 (2009), 97–106. | DOI | MR | Zbl

[12] Tunç, C.: Some stability and boundedness conditions for non-autonomous differential equations with deviating arguments. E. J. Qualitative Theory of Diff. Equ. 2010, 1 (2005), 1–12. | MR

[13] Tunç, C.: Stability and boundedness of solutions of nonlinear differential equations of third-order with delay. Differential Equations and Control Processes 2007, 3 (2007), 1–13. | MR

[14] Yoshizawa, T.: Stability theory by Liapunov’s second method. The Mathematical Society of Japan, Tokyo, 1966. | MR

[15] Zhu, Y. F.: On stability, boundedness and existence of periodic solution of a kind of third order nonlinear delay differential system. Ann. Differential Equations 8, 2 (1992), 249–259. | MR | Zbl