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 JAMP  Vol.4 No.1 , January 2016
Stability and Boundedness of Solutions of Certain Non-Autonomous Third Order Nonlinear Differential Equations
Abstract: In this paper, by defining an appropriate Lyapunov functional, we obtain sufficient conditions for which all solutions of certain real non-autonomous third order nonlinear differential equations are asymptotically stable and bounded. The results obtained improve and extend some known results in the literature.
Cite this paper: Olutimo, A. and Akinwole, F. (2016) Stability and Boundedness of Solutions of Certain Non-Autonomous Third Order Nonlinear Differential Equations. Journal of Applied Mathematics and Physics, 4, 149-155. doi: 10.4236/jamp.2016.41018.
References

[1]   Chin, P.S.M. (1989) Stability Results for the Solution of Certain Fourth Order Autonomous Differential Equations. International Journal of Control, 49, 1163-1173.
http://dx.doi.org/10.1080/00207178908559698

[2]   Reissig, R., Sansone, G. and Conti, R. (1974) Nonlinear Differntial Equations of Higher Order. Noordhoff International Publication, Leyden.

[3]   Chukwu, E.N. (1975) On the Boundedness of Solutions of Third Order Differential Equations. Annali di Matematica Pura ed Applicata, 104, 123-149.
http://dx.doi.org/10.1007/BF02417013

[4]   Ezeilo, J.O.C. (1967) A Generalization of a Boundedness Theorem for a Certain Third-Order Differential Equation. Mathematical Proceedings of the Cambridge Philosophical Society, 63, 735-742.
http://dx.doi.org/10.1017/S0305004100041736

[5]   Harrow, M. (1968) Further Results for the Solutions of Certain Third-Order Differential Equations. Journal London Mathematical Society, 43, 587-592.
http://dx.doi.org/10.1112/jlms/s1-43.1.587

[6]   Omeike, M.O. (2007) Further Results on Global Stability of Third Order Nonlinear Differential Equations. Nonlinear Analysis, 67, 3394-3400.
http://dx.doi.org/10.1016/j.na.2006.10.021

[7]   Omeike, M.O. (2008) New Result in the Ultimate Boundedness of Solutions of a Third Order Non-Linear Ordinary Differential Equation. Journal of Inequalities in Pure & Applied Mathematics, 9, Article 15.8.

[8]   Tunc, C. (2010) The Boundedness of Solutions to Nonlinear Third Order Differential Equations. Nonlinear Dynamics and Systems Theory, 10, 97-102.

[9]   Hara, T. (1971) On the Stability of Soltutions of Certain Third Ordinary Differential Equations. Proceedings of the Japan Academy, 47, 903-908.
http://dx.doi.org/10.3792/pja/1195526293

[10]   Hara, T. (1974) On the Asymptotic Behavior of the Solutions of Some Third and Fourth Order Non-Autonomous Differential Equations. Publications of the Research Institute for Mathematical Sciences, 9, 649-673.
http://dx.doi.org/10.2977/prims/1195192447

[11]   Hara, T. (1975) On the Asymptotic Behavior of Solutions of Certain Non-Autonomous Differential Equations. Osaka Journal of Mathematics, 12, 267-282.

[12]   Mehri, B. and Shadman, D. (1999) Boundedness of Solutions of Certain Third Order Differential Equation. Mathematical Inequalities & Applications, 2, 545-549.
http://dx.doi.org/10.7153/mia-02-45

[13]   Qian, C. (2000) On Global Stability of Third Order Nonlinear Differential Equations. On Global Stability of Third Order Nonlinear Differential Equations, 42, 651-661.

[14]   Omeike, M.O. (2010) New Results on the Asymptotic Behavior of a Third Order Nonlinear Differential Equation. Differential Equations and Applications, 2, 39-51.

[15]   Tunc, C. (2005) Boundedness of Solutions of a Third-Order Nonlinear Differential Equations. Journal of Inequalities in Pure & Applied Mathematics, 6, Article 3, 1-6.

 
 
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