Geodesic
Stability, boundedness and asymptotic behaviour of solutions of certain nonlinear differential equations of the third order
Kragujevac Journal of Mathematics, Tome 35 (2011) no. 3, p. 431 .

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Criteria are established for uniform asymptotic stability, boundedness, uniform ultimate boundedness and asymptotic behaviour of solutions of certain third order nonlinear differential equations with the restoring nonlinear terms depend on $t$ and multiplied by functions of $t$. By constructing a complete Lyapunov function, Lyapunov second method, the technique of Antoisewicz [8] and the limit point of Yoshizawa [22] are employed to obtain the results. Recent results on third order nonlinear differential equations and the results which have been discussed in [16] are special cases of our results.
Classification : 34A34 34D20 34D99
Keywords: Third order differential equations, uniform asymptotic stability, uniform ultimate boundedness, complete Lyapunov function, asymptotic behaviour 
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A. T. Ademola; P. O. Arawomo. Stability, boundedness and asymptotic behaviour of solutions of certain nonlinear differential equations of the third order. Kragujevac Journal of Mathematics, Tome 35 (2011) no. 3, p. 431 . http://geodesic.mathdoc.fr/item/KJM_2011_35_3_a6/