| Title:
|
Stability and Boundednessof the Solutions of Non Autonomous Third Order Differential Equations with Delay (English) |
| Author:
|
Remili, Moussadek |
| Author:
|
Oudjedi, Lynda Damerdji |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
53 |
| Issue:
|
2 |
| Year:
|
2014 |
| Pages:
|
139-147 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Stability |
| Keyword:
|
Lyapunov functional |
| Keyword:
|
delay differential equations |
| Keyword:
|
third-order differential equations |
| MSC:
|
34C11 |
| MSC:
|
34D20 |
| idZBL:
|
Zbl 1317.34157 |
| idMR:
|
MR3331011 |
| . |
| Date available:
|
2014-12-16T15:12:49Z |
| Last updated:
|
2020-01-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144044 |
| . |
| Reference:
|
[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. Zbl 0635.34001, MR 0837654 |
| Reference:
|
[2] Burton, T. A., Makay, G.: Asymptotic stability for functional differential equations. Acta Math. Hung. 65, 3 (1994), 243–251. Zbl 0805.34068, MR 1281434, 10.1007/BF01875152 |
| Reference:
|
[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 2934271 |
| Reference:
|
[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 2766411 |
| Reference:
|
[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. Zbl 1199.34390, MR 2510712 |
| Reference:
|
[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. Zbl 1075.34075, MR 2148124 |
| Reference:
|
[7] Sadek, A. I.: Stability and Boundedness of a Kind of Third-Order Delay Differential System. Applied Mathematics Letters 16, 5 (2003), 657–662. Zbl 1056.34078, MR 1986031, 10.1016/S0893-9659(03)00063-6 |
| Reference:
|
[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. Zbl 0164.39103, MR 0236482, 10.1112/jlms/s1-44.1.347 |
| Reference:
|
[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. Zbl 1139.34054, MR 2368199 |
| Reference:
|
[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. Zbl 1077.34052, 10.1155/JAMSA.2005.29 |
| Reference:
|
[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. Zbl 1176.34064, MR 2511159, 10.1007/s11071-008-9423-6 |
| Reference:
|
[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 2577154 |
| Reference:
|
[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 2384532 |
| Reference:
|
[14] Yoshizawa, T.: Stability theory by Liapunov’s second method. The Mathematical Society of Japan, Tokyo, 1966. MR 0208086 |
| Reference:
|
[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. Zbl 0758.34072, MR 1190138 |
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