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On the behaviour of solutions for a class of third order neutral delay differential equations
(2019) Ademola, T. A.; Mahmoud, A. M.; Arawomo, P. O.
In this paper, a new class of third order nonlinear neutral delay differential equations is discussed. By reducing the third order nonlinear neutral delay differential equations to systems of first order, the second method of Lyapunov is engaged by constructing a complete Lyapunov functional and used to establish criteria that guarantee uniform asymptotic stability of the trivial solution and uniform ultimate boundedness of solutions. The obtained results are not only new but also include many outstanding results in the literature. Finally, the correctness and effectiveness of the obtained results are justified with examples.
Stability, boundedness and existence of periodic solutions to certain third order nonlinear differential equations
(Palacký University Olomouc, 2015) Ademola, T. A.; Ogundiran, M. O.; Arawomo, P. O.
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.