scholarly works
Permanent URI for this collectionhttps://repository.ui.edu.ng/handle/123456789/410
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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 Oscillation of solutions to a generalized forced nonlinear conformable fractional differential equation(2019) Ogunbanjo, A.; Arawomo, P.By using averaging functions, we present some new oscillation criteria for the solution of a generalized forced nonlinear conformable fractional differential equation. The results obtained here extend and improve on some existing results. Examples are also given to show the validity of our results.Item Hyers-ulam stability of a perturbed generalised lienard equation(Academic Publications, Ltd., 2019) Fakunle, I.; Arawomo, P. O.In this paper, we consider the Hyers-Ulam stability of a perturbed generalized Lienard equation, using a nonlinear extension of Gronwall-Bellman integral inequality called the Bihari integral inequality.Item On hyers-ulam stability of nonlinear second order ordinary and functional differential equations(Academic Publications, Ltd., 2018) Fakunle, I.; Arawomo, P. O.In this paper, we consider the Hyers-Ulam stability of some nonlinear second order ordinary and functional differential equations. As mathematical technique, we use some nonlinear extension of the Gronwall integral inequality.Item Hyers-ulam stability of certain class of nonlinear second order differential equations(Research India Publications, 2018) Fakunle, I.; Arawomo, P. O.We investigate the Hyers-Ulam stability of certain classes of nonlinear second order differential equations using a nonlinear generalisation of Gronwall-Bellman integral inequality known as Bihari integral inequality.Item Existence of positive solutions for a coupled system of nonlinear boundary value problems of fractional order with integral boundary conditions(Academic Publications, 2017) Akorede, M. B.; Arawomo, P. O.In this work, we discuss the existence of positive solutions for a coupled system of nonlinear boundary value problems of fractional order with integral boundary conditions. The existence result is obtained by means of Krasnosel’skii fixed-point theorem in a cone.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 Positive solutions to a nonlinear eigenvalue problem of fractional differential equation with integro-differential boundary conditions(Academic Publications, Ltd., 2017) Akorede, M. B.; Arawomo, P. O.In this paper, we establish the existence of positive solutions for eigenvalue problem of fractional differential equations with integro-differential boundary conditions. We determine the intervals of parameter _ for which the existence of positive solutions is guaranteed. An example is also presented to show the application 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 Positive solutions for a coupled system of nonlinear second order eigenvalue problems(2015) Akorede, M. B.; Arawomo, P. O.In this work, we consider a system of coupled nonlinear second order eigenvalue problems. Under suitable conditions, existence of positive solutions are established, for determined eigenvalues, by the use of abstract fixed-point.