Stability of the solutions of nonlinear third order differential equations with multiple deviating arguments

Moussadek Remili; Lynda Damerdji Oudjedi

doi:10.1515/ausm-2016-0009

.blurhash-client-img { display: none !important; }

Stability of the solutions of nonlinear third order differential equations with multiple deviating arguments

Acta Universitatis Sapientiae, Mathematica

Volume 8 (2016): Issue 1 (August 2016)

By: Moussadek Remili and Lynda Damerdji Oudjedi

Open Access

|Aug 2016

Abstract

In this paper, with use of Lyapunov functional, we investigate asymptotic stability of solutions of some nonlinear differential equations of third order with delay. Our results include and improve some well-known results in the literature.

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.
Search in Google Scholar
[2] T. A. Burton, Volterra Integral and Differential Equations, Mathematics in Science and Engineering V(202) (2005), 2nd edition.
Search in Google Scholar
[3] L. É. Él’sgol’ts, Introduction to the theory of differential equations with deviating arguments, Translated from the Russian by Robert J. McLaughlin Holden-Day, Inc., San Francisco, Calif. London-Amsterdam, 1966.
Search in Google Scholar
[4] M. O. Omeike, New results on the stability of solution of some non-autonomous delay differential equations of the third order, Differential Equations and Control Processes, 1 (2010), 18–29.
Search in Google Scholar
[5] 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), 49–58.10.2478/v10157-010-0026-4
Open DOI Search in Google Scholar
[6] M. Remili, D. Beldjerd. On the asymptotic behavior of the solutions of third order delay differential equations, Rend. Circ. Mat. Palermo63 (2014), 447–455.10.1007/s12215-014-0169-3
Open DOI Search in Google Scholar
[7] M. Remili, L. Damerdji Oudjedi, Stability and Boundedness of the Solutions of Non Autonomous Third Order Differential Equations with Delay, Acta Univ. Palacki. Olomuc., Fac. rer. nat., Mathematica, 53 (2) (2014), 139–147.
Search in Google Scholar
[8] A. I. Sadek, On the Stability of Solutions of Some Non-Autonomous Delay Differential Equations of the Third Order, Asymptot. Anal., 43 (1-2) (2005),1–7.
Search in Google Scholar
[9] A. I. Sadek, Stability and Boundedness of a Kind of Third-Order Delay Differential System, Applied Mathematics Letters, 16 (5) (2003), 657–662.10.1016/S0893-9659(03)00063-6
Open DOI Search in Google Scholar
[10] K. Swick, On the boundedness and the stability of solutions of some non-autonomous differential equations of the third order, J. London Math. Soc.44 (1969), 347–359.10.1112/jlms/s1-44.1.347
Open DOI Search in Google Scholar
[11] C. Tunç, On asymptotic stability of solutions to third order nonlinear differential equations with retarded argument, Communications in applied analysis, 11 (4) (2007), 515–528.
Search in Google Scholar
[12] C. Tunç, On the stability and boundedness of solutions to third order nonlinear differential equations with retarded argument, Nonlinear Dynam.57 (1-2) (2009), 97–106.10.1007/s11071-008-9423-6
Open DOI Search in Google Scholar
[13] C. Tunç, Some stability and boundedness conditions for non-autonomous differential equations with deviating arguments, E. J. Qualitative Theory of Diff. Equ., 1 (2010), 1–12.
Search in Google Scholar
[14] C. Tunç, Stability and boundedness of solutions of nonlinear differential equations of third-order with delay, Journal Differential Equations and Control Processes (Differentsialprimnye Uravneniyai Protsessy Upravleniya), 3 (2007), 1–13.
Search in Google Scholar
[15] C. Tunç, M. Gözen, Stability and Uniform Boundedness in Multidelay Functional Differential Equations of Third Order, Hindawi Publishing Corporation Abstract and Applied Analysis. Volume 2013, Article ID 248717, 7 pages.10.1155/2013/248717
Open DOI Search in Google Scholar
[16] T. Yoshizawa, Stability theory by Liapunov’s second method, The Mathematical Society of Japan, Tokyo, 1966.
Search in Google Scholar
[17] 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), 249–259.
Search in Google Scholar

Articles in this issue

DOI: https://doi.org/10.1515/ausm-2016-0009 | Journal eISSN: 2066-7752

Journal RSS Feed

Language: English

Page range: 150 - 165

Submitted on: Jan 28, 2015

Published online: Aug 2, 2016

Published in print: Aug 1, 2016

Published by: Sapientia Hungarian University of Transylvania

In partnership with: Paradigm Publishing Services

Keywords:

stability,

Lyapunov functional,

delay differential equations,

third-order differential equations

MSC:

34C11,

34D20

Related subjects:

Mathematics,

General mathematics

© 2016 Moussadek Remili, Lynda Damerdji Oudjedi, published by Sapientia Hungarian University of Transylvania
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 8 (2016): Issue 1 (August 2016)