ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

Generalization of Some Qualitative Behaviour of Solutions of Third Order Nonlinear Differential Equations

Author(s):

A. T. Ademola

Department of Mathematics,
University of Ibadan, Ibadan, Nigeria

ademola672000@yahoo.com

P. O. Arawomo

Department of Mathematics,
University of Ibadan, Ibadan, Nigeria

womopeter@gmail.com

Abstract:

Criteria for uniform asymptotic stability, boundedness, uniform ultimate boundedness and asymptotic behaviour of solutions of the most general third order nonlinear differential equations with the restoring nonlinear terms depending explicitly on the independent real variable t are established. The construction a complete Lyapunov function, Lyapunov's second method, the technique introduced by Antoisewicz and the limit point of Yoshizawa are used to obtain the results. The most recent results of Ademola and Arawomo and results on third order nonlinear differential equations which have been discussed in the paper R. Reissig, G. Sansone, R. Conti, Nonlinear differential equations of higher order, (Noordhoff International Publishing Leyeden, 1974) are particular cases of our results.

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