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

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Uniform Stability, Boundedness and Asymptotic Behaviour of Solutions of Some Third Order Nonlinear Delay 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

O. M. Ogunlaran

Department of Mathematics and Statistics
Bowen University, Iwo,
Osun State, Nigeria

dothew2002@yahoo.com

E. A. Oyekan

Department of Mathematics and Statistics
Bowen University, Iwo,
Osun State, Nigeria

shalomfa@yahoo.com

Abstract:

In this paper sufficient conditions for uniform asymptotic stability of the trivial solutions, uniform boundedness, uniform ultimate boundedness and asymptotic behaviour of solutions of some third order nonlinear neutral delay differential equations are established. We employ Lyapunov's direct method by constructing a complete Lyapunov functional to obtain the results. Recent results on third order nonlinear delay differential equations are particular cases of our results.

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