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 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 Stability, boundedness and asymptotic behaviour of solutions of certain nonlinear differential equations of the third order(2011) Ademola, T. A.; Arawomo, P. O.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.Item On the stability and ultimate boundedness of solutions for certain third order differential equations(Science Publications, 2008) Ademola, T. A.; Arawomo, P. O.With respect to our observation in the relevant literature, work on stability and boundedness of solution for certain third order nonlinear differential equations where the nonlinear and the forcing terms depend on certain variables are scare. The objective of this study was to get criteria for stability and boundedness of solutions for these classes of differential equations. Approach: Using Lyapunov second or direct method, a complete Lyapunov function was constructed and used to obtain our results. Results: Conditions were obtained for: (i) Uniform asymptotic stability and, (ii) Uniform ultimate boundedness, of solutions for certain third order non-linear non-autonomous differential equations. Conclusion: Our results do not only bridge the gap but extend some well-known results in the literature.