Mathematics
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Item 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.Item Stability, Boundedness and periodic solutions to certain second order delay differential equations(2017-06) Ademola, T. A.; Arawomo, P. O.; Idowu, A. S.Stability, boundedness and existence of a unique periodic solution to certain second order nonlinear delay differential equations is discussed. By employing Lyapunov’s direct (or second) method, a complete Lyapunov functional is constructed and used to establish sufficient conditions, on the nonlinear terms, that guarantee uniform asymptotic stability, uniform ultimate boundedness and existence of a unique periodic solution. Obtained results complement many outstanding recent results in the literature. Finally, examples are given to show the effectiveness of our method and correctness of our results.Item 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.Item Uniform stability, boundedness and asymptotic behaviour of solutions of some third order nonlinear delay di erential equations(2013) Ademola, T. A.; Arawomo, P. O.; Ogunlaran, O. M.; Oyekan, E. A.Item On the asymptotic behaviour of solutions of certain differential equations of the third order(2014-03) Ademola, T. A.; Arawomo, P. O.In this article, Lyapunov second method is used to obtain criteria for uniform ultimate boundedness and asymptotic behaviour of solutions of nonlinear differential equations of the third order. The results obtained in this investigation include and extend some well known results on third order nonlinear differential equations in the literature.Item Uniform stability and boundedness of solutions of nonlinear delay differential equations of the third order(2013) Ademola, T. A.; Arawomo, P. O.In this paper, a complete Lyapunov functional was constructed and used to obtain criteria (when p = 0) for uniform asymptotic stability of the zero solution of the nonlinear delay differential equation (1.1). When p ≠ 0, sufficient conditions are also established for uniform boundedness and uniform ultimate boundedness of solutions of this equation. Our results improve and extend some well known results in the literature.Item Generalization of some qualitative behaviour of Solutions of third order nonlinear differential equations(2012) Ademola, T. A.; Arawomo, P. O.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 [9] and the limit point of Yoshizawa [29] are used to obtain the results. The most recent results of Ademola and Arawomo [1, 2, 3, 4] and results on third order nonlinear differential equations which have been discussed in [18] are particular cases of our results.Item Boundedness and asymptotic behaviour of solutions of a nonlinear differential equation of the third order(2012) Ademola, T. A.; Arawomo, P. O.In this paper, we use Lyapunov second method. A complete Lyapunov function was constructed and used to obtain criteria for boundedness, uniform ultimate boundedness and asymptotic behaviour of solutions of a nonlinear differential equation of the third order. Our results revise, improve and extend existing results on boundedness, uniform ultimate boundedness and asymptotic behaviour of solutions of third order nonlinear differential equations in the literature.Item Stability and uniform ultimate boundedness of solutions of some third-order differential equations(Nyregyhazi Foiskola/College of Nyregyhaza, 2011) Ademola, T. A.; Arawomo, P. O.The paper is concerned with the stability and uniform ultimate boundedness for all solutions of a third order nonlinear differential equations (1.1). Sufficient conditions under which all solutions x(t), its first and second derivatives tend to zero as t → ∞ are given.Item Asymptotic behaviour of solutions of third order nonlinear differential equations(2011) Ademola, T. A.; Arawomo, P. O.In this paper, Lyapunov direct method was employed. We present criteria for all solutions x(t) its first and second derivatives of the third order nonlinear non autonomous differential equations to con- verge to zero as t → ∞. Sufficient conditions are also established for the boundedness and uniform ultimate boundedness of solutions of the equations considered. Our results revise, improve and generalize existing results in the literature.