scholarly works
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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.Item Blow up for a viscoelastic wave equation with space-time potential in Rn(2022-07) Ogbiyele, P. A.; Arawomo, P. O.In this paper, we consider the following wave equation: with space-time dependent potential, where the initial data have compact support. Under suitable assumptions on the nonlinear function f, the relaxation function g and the damping potential b, we obtain blow up results using the perturbed energy method.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 Boundedness and stability of solutions of some nonlinear differential equations of the third-order(2009) Ademola, T. A.; Arawomo, P. O.Sufficient conditions are established for the uniform ultimate boundedness of solutions of a third-order nonlinear differential equation (1). When, p(t,x,x',x")=0, criteria under which all solutions x(t), its first and second derivatives tend to zero as t→∞, are given.Item Boundedness results for a certain third order nonlinear differential equation(Elsevier Inc., 2010) Ademola, T. A.; Ogundiran, M. O.; Arawomo, P. O.; Adesina, O. A.Sufficient conditions for the existence of solutions to boundedness and ultimate boundedness problems associated to a certain third order nonlinear differential equation are given by means of the Lyapunov’s second method. The appropriate Lyapunov function is given explicitly. Our results complement some well known results on the third order differential equations in the literature.Item Energy decay for a viscoelastic wave equation with space-time potential in Rn(Elsevier Inc., 2022) Ogbiyele, P. A.; Arawomo, P. O.In this paper, we consider the following viscoelastic wave equation with space-time dependent potential and where the initial data u0(x), u1(x)have compact support. Under suitable assumptions on the relaxation function g and the potential b, we obtain a more general energy decay result using the perturbed energy method.Item Existence and Blow up Time Estimate for a negative initial energy solution of a nonlinear cauchy problem(Springer Nature B.V., 2020-06) Ogbiyele, P. A.; Arawomo, P. O.In this paper, we consider nonlinear wave equations with dissipation having the form utt −div_(|∇u|γ−2∇u)+b(t, x)|ut |m−2ut = g(x,u) for (t, x) ∈ [0,∞) × Rn. We obtain existence and blow up results under suitable assumptions on the positive function b(t, x) and the nonlinear function g(x,u). The existence result was obtained using the Galerkin approach while the blow up result was obtained via the perturbed energy method. Our result improves on the perturbed energy technique for unbounded domains.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 Existence results for some interval differential equations(American Mathematical Society, 2000) Arawomo, P. O.This paper is concerned with the problem of existence of solutions to interval differential equations which result from attempts to provide a concide interval solution to some differential equations with inexact data or parameters contained in an interval. An extension of the interval iterative scheme of Moore is used to establish the main results which include those of Sveloslav Merkov’s.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 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 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 An Interval Analytic method for a nonlinear boundary value problem describing transport process(Academic Publications Ltd., 2010-05) Arawomo, P. O.In recent times, the methods of interval analysis have been successfully employed to establish existence results for the solution of initial value problems. In this paper, we extend the methods to establish existence of solution for a special boundary value problem. A particular case of this problem describes equations arising in transport processItem An interval analytic method in constructive existence theorems for initial value problems(Dynamic Publishers, 2002) Arawomo, P. O.; Akinyele, O.The method of interval analysis is employed to show that the solution, if it exists, of a first order initial value problem is majorised by an interval function whose end- functions satisfy some prescribed conditions. An interval operator is constructed and shown to be a contraction on the majorising interval function. Using this operator, the existence and uniqueness of the solution is established.Item Interval analytic method in existence result for hyperbolic partial differential equation(2014-04) Arawomo, P. O.Without the usual assumption of monotonicity, we establish some results on the theory of hyperbolic differential inequalities which enable us to produce a majorising interval function for the solution of the hyperbolic initial value problem. Using this function, a variation of parameters formula and interval iterative technique, the existence of solution to the problem is established.Item Interval valued extension of wendroff type integral inequalities(Elsevier, 2009) Arawomo, P. O.In this paper we extend the theory of integral inequalities to interval valued mappings in two independent variables. By this, set inclusions are used instead of partial order relation and this enables us to obtain simultaneous upper and lower bounds instead of a pair of inequalities.Item On asymptotic behavior of solution to a nonlinear wave equation with space-time speed of propagation and damping terms(2021-12) Ogbiyele, P. A.; Arawomo, P. O.In this paper, we consider the asymptotic behavior of solution to the nonlinear damped wave equationutt − div¡a(t, x)∇u¢+ b(t, x)ut = −|u|p−1u t ∈ [0, ∞), x ∈ Rn u(0, x) = u0(x), ut(0, x) = u1(x) x ∈ Rn with space-time speed of propagation and damping potential. We obtained L2 decay estimates via the weighted energy method and under certain suitable assumptions on the functions a(t, x) and b(t, x). The technique follows that of Lin et al.[8] with modification to the region of consideration in Rn. These decay result extends the results in the literature.Item On blow up of positive initial energy solution of a nonlinear wave equation with nonlinear source and boundary damping terms(2021-08) Ogbiyele, P. A.; Arawomo, P. O.In this paper, we consider a nonlinear wave equation having nonlinear source and boundary damping terms and obtain blow up results under certain polynomial growth conditions on y, r, m and p, where the polynomial growth order of the nonlinear functions g and / are p + 1 and to +1 respectively. We obtain the blow up result using the perturbed energy technique.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 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.