Geodesic
Stability, Boundedness and Existenceof Periodic Solutions to Certain Third Order Nonlinear Differential Equations
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 54 (2015) no. 1, pp. 5-18.

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In this paper, criteria are established for uniform stability, uniform ultimate boundedness and existence of periodic solutions for third order nonlinear ordinary differential equations. In the investigation Lyapunov’s second method is used by constructing a complete Lyapunov function to obtain our results. The results obtained in this investigation complement and extend many existing results in the literature.
Classification : 34C25, 34D20, 34D40, 65L06
Keywords: Third order; nonlinear differential equation; uniform stability; uniform ultimate boundedness; periodic solutions 
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ADEMOLA, A. T.; OGUNDIRAN, M. O.; ARAWOMO, P. O. Stability, Boundedness and Existenceof Periodic Solutions to Certain Third Order Nonlinear Differential Equations. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 54 (2015) no. 1, pp. 5-18. http://geodesic.mathdoc.fr/item/AUPO_2015__54_1_a0/