Previous |  Up |  Next

Article

Title: Boundedness and stability in third order nonlinear differential equations with multiple deviating arguments (English)
Author: Remili, Moussadek
Author: Oudjedi, Lynda D.
Language: English
Journal: Archivum Mathematicum
ISSN: 0044-8753 (print)
ISSN: 1212-5059 (online)
Volume: 52
Issue: 2
Year: 2016
Pages: 79-90
Summary lang: English
.
Category: math
.
Summary: In this paper, we establish some new sufficient conditions which guarantee the stability and boundedness of solutions of certain nonlinear and non autonomous differential equations of third order with delay. By defining appropriate Lyapunov function, we obtain some new results on the subject. By this work, we extend and improve some stability and boundedness results in the literature. (English)
Keyword: Lyapunov functional
Keyword: delay differential equations
Keyword: third-order differential equations
MSC: 34C11
MSC: 34D20
idZBL: Zbl 06644060
idMR: MR3535630
DOI: 10.5817/AM2016-2-79
.
Date available: 2016-07-19T11:26:38Z
Last updated: 2018-01-10
Stable URL: http://hdl.handle.net/10338.dmlcz/145747
.
Reference: [1] Ademola, A.T., Arawomo, P.O.: Uniform stability and boundedness of solutions of nonlinear delay differential equations of third order.Math. J. Okayama Univ. 55 (2013), 157–166. MR 3026962
Reference: [2] Ademola, A.T., Arawomo, P.O., Ogunlaran, O.M., Oyekan, E.A.: Uniform stability, boundedness and asymptotic behaviour of solutions of some third order nonlinear delay differential equations.Differential Equations and Control Processes N4 (2013), 43–66. MR 3567041
Reference: [3] Afuwape, A.U., Omeike, M.O.: On the stability and boundedness of solutions of a kind of third order delay differential equations.Appl. Math. Comput. 200 Issue 1 (2008), 444–451. Zbl 1316.34070, MR 2421659, 10.1016/j.amc.2007.11.037
Reference: [4] Afuwape, A.U., Omeike, M.O.: Stability and boundedness of solutions of a kind of third-order delay differential equations.Computational and Applied Mathematics 29 (3) (2010), 329–342. Zbl 1216.34068, MR 2740657, 10.1590/S1807-03022010000300001
Reference: [5] Agarwal, R., O’Regan, D.: Singular problems modelling phenomena in the theory of pseudoplastic fluids.ANZIAM J. 45 (2003), 167–179. Zbl 1201.35155, MR 2017741, 10.1017/S1446181100013249
Reference: [6] Bai, Y., Guo, C.: New results on stability and boundedness of third order nonlinear delay differential equations.Dynam. Systems Appl. 22 (1) (2013), 95–104. Zbl 1302.34107, MR 3098746
Reference: [7] Burton, T.A.: Stability and periodic solutions of ordinary and functional differential equations.Math. Sci. Engrg. 178 (1985). Zbl 0635.34001, MR 0837654
Reference: [8] Burton, T.A.: Volterra Integral and Differential Equations.Math. Sci. Engrg. 202 (2005), 2nd edition. Zbl 1075.45001, MR 2155102
Reference: [9] Élsgolts, L. É.: Introduction to the theory of differential equations with deviating arguments.London-Amsterdam, 1966, Translated from the Russian by Robert J. McLaughlin Holden-Day,Inc.,San Francisco, Calif. MR 0192154
Reference: [10] Gregus, M.: Third Order Linear Differential Equations.Reidel, Dordrecht, 1987. Zbl 0602.34005, MR 0882545
Reference: [11] Juan, Zhang Li, Geng, Si Li: Globally asymptotic stability of a class of third order nonlinear system.Acta Math. Appl. Sinica 30 (1) (2007), 99–103. MR 2339313
Reference: [12] Omeike, M.O.: Stability and boundedness of solutions of some non-autonomous delay differential equation of the third order.An. Ştiinţ. Univ. Al. I. Cuza Iaşi Mat. (N.S.) 55 (1) (2009), 49–58. Zbl 1199.34390, MR 2510712
Reference: [13] 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 1 (2010), 18–29. MR 2766411
Reference: [14] O’Regan, D.: Topological Transversality: Application to third-order boundary value problem.SIAM. J. Math. Anal. 18 (3) (1987), 630–641. MR 0883557, 10.1137/0518048
Reference: [15] Oudjedi, L., Beldjerd, D., Remili, M.: On the stability of solutions for non-autonomous delay differential equations of third-order.Differential Equations and Control Processes 1 (2014), 22–34. Zbl 1357.34071, MR 3570433
Reference: [16] Remili, M., Beldjerd, D.: On the asymptotic behavior of the solutions of third order delay differential equations.Rend. Circ. Mat. Palermo 63 (2014), 447–455. Zbl 1321.34097, MR 3298595, 10.1007/s12215-014-0169-3
Reference: [17] Remili, M., Oudjedi, L.D.: Stability and boundedness of the solutions of non autonomous third order differential equations with delay.Acta Univ. Palack. Olomuc. Fac. Rerum Natur. Math. 53 (2) (2014), 139–147. MR 3331011
Reference: [18] Sadek, A.I.: Stability and boundedness of a kind of third-order delay differential system.Appl. Math. Lett. 16 (5) (2003), 657–662. Zbl 1056.34078, MR 1986031, 10.1016/S0893-9659(03)00063-6
Reference: [19] Sadek, A.I.: On the stability of solutions of somenon-autonomous delay differential equations of the third order.Asymptot. Anal. 43 (2) (2005), 1–7. MR 2148124
Reference: [20] 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: [21] Tunç, C.: Stability and boundedness of solutions of nonlinear differential equations of third-order with delay.J. Differential Equations and Control Processes 3 (2007), 1–13. MR 2384532
Reference: [22] Tunç, C.: On the stability of solutions for non-autonomous delay differential equations of third-order.Iran. J. Sci. Technol. Trans. A Sci. 32 (4) (2008), 261–273. Zbl 1364.34107, MR 2683011
Reference: [23] Tunç, C.: Boundedness in third order nonlinear differential equations with bounded delay.Bol. Mat. (N.S.) 16 (1) (2009), 1–10. Zbl 1256.34055, MR 2891067
Reference: [24] Tunç, C.: On the stability and boundedness of solutions to third order nonlinear differential equations with retarded argument.Nonlinear Dynam. 57 (1–2) (2009), 97–106. Zbl 1176.34064, MR 2511159, 10.1007/s11071-008-9423-6
Reference: [25] Tunç, C.: Stability criteria for certain third order nonlinear delay differential equations.Portugal. Math. 66 (1) (2009), 71–80. Zbl 1166.34329, MR 2512821, 10.4171/PM/1831
Reference: [26] Tunç, C.: Some stability and boundedness conditions for non-autonomous differential equations with deviating arguments.Electron. J. Qual. Theory Differ. Equ. 1 (2010), 1–12. Zbl 1201.34123, MR 2577154, 10.14232/ejqtde.2010.1.1
Reference: [27] Tunç, C.: Stability and bounded of solutions to non-autonomous delay differential equations of third order.Nonlinear Dynam. 62 (2010), 945–953. Zbl 1215.34079, MR 2745954, 10.1007/s11071-010-9776-5
Reference: [28] Tunç, C.: Stability and boundedness of the nonlinear differential equations of third order with multiple deviating arguments.Afrika Mat. (3) 24 (3) (2013), 381–390. Zbl 1291.34111, MR 3090565, 10.1007/s13370-012-0067-9
Reference: [29] Tunç, C.: On the stability and boundedness of certain third order non-autonomous differential equations of retarded type.Proyecciones 34 (2) (2015), 147–159. Zbl 1332.34115, MR 3358608, 10.4067/S0716-09172015000200004
Reference: [30] Tunç, C., Gözen, M.: Stability and uniform boundedness in multidelay functional differential equations of third order.Abstr. Appl. Anal. 7 (2013), 1–8. Zbl 1276.34058, MR 3055944
Reference: [31] Yao, H., Wang, J.: Globally asymptotic stability of a kind of third-order delay differential system.Int. J. Nonlinear Sci. 10 (1) (2010), 82–87. Zbl 1235.34198, MR 2721073
Reference: [32] Zhang, Z., Wang, J., Shi, W.: A boundary layer problem arising in gravity-driven laminar film flow of power-law fluids along vertical walls.Z. Angew. Math. Phys. 55 (5) (2004), 169–780. Zbl 1059.76007, MR 2087764, 10.1007/s00033-004-1122-7
Reference: [33] Zhao, J., Deng, Y.: Asymptotic stability of a certain third-order delay differential equation.J. Math. (Wuhan) 34 (2) (2014), 319–323. MR 3202424
Reference: [34] 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
.

Files

Files Size Format View
ArchMathRetro_052-2016-2_2.pdf 505.2Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo