Geodesic
On Stability and Boundedness properties of solutions of certain second order non-autonomous nonlinear ordinary differential equation
Kragujevac Journal of Mathematics, Tome 39 (2015) no. 2, p. 255 .

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In this paper, sufficient criteria for the existence of solutions to uniform asymptotic stability and boundedness problems associated with certain second order nonlinear non autonomous ordinary differential equation are established with the aid of Lyapunov's direct method. Furthermore, the appropriate complete Lyapunov function is given explicitly. Our results complement some well known results on the second order differential equations in the literature.
Classification : 34A34, 34D20, 34D23 34D99
Keywords: Asymptotic stability, boundedness, Lyapunov function, nonlinear, non autonomous, differential equation 
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     author = {J. G. Alaba and B. S. Ogundare},
     title = {On {Stability} and {Boundedness} properties of solutions of certain second order non-autonomous nonlinear ordinary differential equation},
     journal = {Kragujevac Journal of Mathematics},
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J. G. Alaba; B. S. Ogundare. On Stability and Boundedness properties of solutions of certain second order non-autonomous nonlinear ordinary differential equation. Kragujevac Journal of Mathematics, Tome 39 (2015) no. 2, p. 255 . http://geodesic.mathdoc.fr/item/KJM_2015_39_2_a11/