ASYMPTOTIC STABILITY AND BOUNDEDNESS OF SOLUTION OF 3rd ORDER NONLINEAR DIFFERENTIAL EQUATION
Keywords:
Nonlinear:, asymptotical stability:, boundedness, Lyapunov function:
Abstract
In this paper by using the Lyapunov function we investigate the asymptotical stability and boundedness of solution or 3rd order nonlinear differential equation. By using Lyapunov direct method to determine the asymptotic stability and bounded of solution for nonlinear differential equation by using a suitable Lyapunov function.
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References
1] E.A. Barbashin: Lyapunov functions, Izdat. Nauka, Moscow, 1970.
[2] Ezeilo J.O.C: Further Results of Solutions of a Third Order Differential Equations, Proc. Cambridge Philos. Soc. 59 (1963), 111-116.
[3] Ezeilo J.O.C: A Stability Result for a Certain Third-Order Differential Equations, Ann. Mat. Pura Appl (4) 72 (1966), 1-9.
[4] B.S. Ogundare: Further Results on United Qualitative Properties of Solution of Certain Third Order Non-Linear Differential Equations. IJPAM, Vol.46, No.5,(2008),627-636.
[5] C. Qian: On Global Stability of Third Order Nonlinear Differential Equations. Nonlinear Analysis 42 (2000), 651-661.
[6] Cemil Tunç and Muzaffer Ateş: Stability and Boundedness Results for Solutions of Certain Third Order Nonlinear Vector Differential Equations, Nonlinear Dynamics , ugust 2006, Volume 45, Issue 3–4, pp 273–281.
[7] A.U. AFUWAPE and M.O. OMEIKE: Stability and boundedness of solutions of a kind of third-order delay differential equations*,Volume 29, N. 3, pp. 329–342, 2010, Copyright © 2010 SBMAC, ISSN 0101-8205, Comput. Appl. Math. vol.29 no.3 São Carlos 2010.
[8] Pane M. RemiliD Beldjerd : Stability and ultimate boundedness of solutions of some third order differential equations with delay,Journal of the Association of Arab Universities for Basic and Applied Sciences, Volume 23, June 2017, Pages 90-95.
[9] A. T. Ademola and P. O. Arawomo: Stability, Boundedness and periodic solutions to certain second order delay differential equations Obafemi Awolowo University, Nigeria University of Ibadan, Nigeria, Proyecciones Journal of Mathematics, Vol. 36, No 2, pp. 257-282, June 2017. Universidad Cat´olica del Norte Antofagasta – Chile
[10] Lynda D. Oudjedi, Moussadek Remili: Boundedness and stability in third order nonlinear vector differential equations with multiple deviating arguments Journal of the Association of Arab Universities for Basic and Applied Sciences,2017.
[2] Ezeilo J.O.C: Further Results of Solutions of a Third Order Differential Equations, Proc. Cambridge Philos. Soc. 59 (1963), 111-116.
[3] Ezeilo J.O.C: A Stability Result for a Certain Third-Order Differential Equations, Ann. Mat. Pura Appl (4) 72 (1966), 1-9.
[4] B.S. Ogundare: Further Results on United Qualitative Properties of Solution of Certain Third Order Non-Linear Differential Equations. IJPAM, Vol.46, No.5,(2008),627-636.
[5] C. Qian: On Global Stability of Third Order Nonlinear Differential Equations. Nonlinear Analysis 42 (2000), 651-661.
[6] Cemil Tunç and Muzaffer Ateş: Stability and Boundedness Results for Solutions of Certain Third Order Nonlinear Vector Differential Equations, Nonlinear Dynamics , ugust 2006, Volume 45, Issue 3–4, pp 273–281.
[7] A.U. AFUWAPE and M.O. OMEIKE: Stability and boundedness of solutions of a kind of third-order delay differential equations*,Volume 29, N. 3, pp. 329–342, 2010, Copyright © 2010 SBMAC, ISSN 0101-8205, Comput. Appl. Math. vol.29 no.3 São Carlos 2010.
[8] Pane M. RemiliD Beldjerd : Stability and ultimate boundedness of solutions of some third order differential equations with delay,Journal of the Association of Arab Universities for Basic and Applied Sciences, Volume 23, June 2017, Pages 90-95.
[9] A. T. Ademola and P. O. Arawomo: Stability, Boundedness and periodic solutions to certain second order delay differential equations Obafemi Awolowo University, Nigeria University of Ibadan, Nigeria, Proyecciones Journal of Mathematics, Vol. 36, No 2, pp. 257-282, June 2017. Universidad Cat´olica del Norte Antofagasta – Chile
[10] Lynda D. Oudjedi, Moussadek Remili: Boundedness and stability in third order nonlinear vector differential equations with multiple deviating arguments Journal of the Association of Arab Universities for Basic and Applied Sciences,2017.
Published
2019-10-29
How to Cite
ABID MOHAMMED, S. (2019). ASYMPTOTIC STABILITY AND BOUNDEDNESS OF SOLUTION OF 3rd ORDER NONLINEAR DIFFERENTIAL EQUATION. Journal of Duhok University, 22(1), 26-29. https://doi.org/10.26682/sjuod.2019.22.1.4
Section
Pure and Engineering Sciences
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