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We establish some new sufficient conditions which guarantee the boundedness and square integrability of solutions of certain third order differential equation. Example is included to illustrate the results. By this work, we extend and improve some results in the literature.

Boundedness and stability in third order nonlinear differential equations with multiple deviating arguments

Moussadek Remili, Lynda D. Oudjedi (2016)

Archivum Mathematicum

In this paper, we establish some new sufficient conditions which guarantee the stability and boundedness of solutions of certain nonlinear and non autonomous differential equations of third order with delay. By defining appropriate Lyapunov function, we obtain some new results on the subject. By this work, we extend and improve some stability and boundedness results in the literature.

Boundedness and unboundedness of solutions of an $n$ -th order differential equation with delayed argument

Vincent Šoltés, Anna Hrubinová (1984)

Archivum Mathematicum

Boundedness criteria for a class of second order nonlinear differential equations with delay

Daniel O. Adams, Mathew Omonigho Omeike, Idowu A. Osinuga, Biodun S. Badmus (2023)

Mathematica Bohemica

We consider certain class of second order nonlinear nonautonomous delay differential equations of the form $a (t) x^{''} + b (t) g (x, x^{'}) + c (t) h (x (t - r)) m (x^{'}) = p (t, x, x^{'})$ and ${(a (t) x^{'})}^{'} + b (t) g (x, x^{'}) + c (t) h (x (t - r)) m (x^{'}) = p (t, x, x^{'}),$ where $a$ , $b$ , $c$ , $g$ , $h$ , $m$ and $p$ are real valued functions which depend at most on the arguments displayed explicitly and $r$ is a positive constant. Different forms of the integral inequality method were used to investigate the boundedness of all solutions and their derivatives. Here, we do not require construction of the Lyapunov-Krasovski functional to establish our results. This work...

Boundedness of solutions of a certain fifth-order nonlinear differential equations

Vladimír Vlček (1989)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Boundedness of solutions of a third-order nonlinear differential equation.

Tunç, Cemil (2005)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

Boundedness of Solutions of Certain System of Second-order Ordinary Differential Equations

Mathew Omonigho Omeike, O. O. Oyetunde, A. L. Olutimo (2014)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

We extend, in this paper, some known results on the boundedness of solutions of certain second order nonlinear scalar differential equations to system of second order nonlinear differential equations.

Boundedness of Solutions of Non-Linear Differential Equation Systems

Pavol Šoltés (1971)

Matematický časopis

Boundedness of solutions of the third order differential equation with oscillatory restoring and forcing terms

Ján Andres (1986)

Czechoslovak Mathematical Journal

Boundedness of solutions to fourth-order differential equation with oscillatory restoring and forcing terms.

Omeike, Mathew O. (2007)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Boundedness of solutions to fourth-order differential equations with oscillatory restoring and forcing terms.

Ogundare, Babatunde S. (2006)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Boundedness of solutions via the twist-theorem

R. Dieckerhoff, E. Zehnder (1987)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Boundedness results of solutions to the equation $x^{\prime\prime\prime}+ax^{\prime\prime}+g(x)x^{\prime}+h(x)=p(t)$ without the hypothesis $h(x)\,\text{sgn}x\geq 0$ $for|x|>R$ .

Ján Andres (1986)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Per l'equazione differenziale ordinaria non lineare del 3° ordine indicata nel titolo, studiata da numerosi autori sotto l'ipotesi $h(x)\,\text{sgn}x\geq 0$ $for|x|>R$

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Boundedness and global stability for a predator-prey system with the Beddington-DeAngelis functional response.

Boundedness and oscillatoriness of solutions of a nonlinear differential equation of the second order

Boundedness and oscillatoriness of solutions of the equation y" + a(x)g(y, y') + b(x)f(y)h(y') = 0

Boundedness and periodicity of Fifth Order non-Linear Differential Equations

Boundedness and square integrability of solutions of certain third-order differential equations