Further ultimate boundedness of solutions of some system of third order nonlinear ordinary differential equations

A. U. Afuwape; Mathew Omonigho Omeike

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2004)

  • Volume: 43, Issue: 1, page 7-20
  • ISSN: 0231-9721

Abstract

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In this paper, we shall give sufficient conditions for the ultimate boundedness of solutions for some system of third order non-linear ordinary differential equations of the form X w i d t h 0 p t h e i g h t 5 . 46 p t t o 8 p t . . . + F ( X ¨ ) + G ( X ˙ ) + H ( X ) = P ( t , X , X ˙ , X ¨ ) where X , F ( X ¨ ) , G ( X ˙ ) , H ( X ) , P ( t , X , X ˙ , X ¨ ) are real n -vectors with F , G , H : ℝ n → ℝ n and P : ℝ × ℝ n × ℝ n × ℝ n → ℝ n continuous in their respective arguments. We do not necessarily require that F ( X ¨ ) , G ( X ˙ ) and H ( X ) are differentiable. Using the basic tools of a complete Lyapunov Function, earlier results are generalized.

How to cite

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Afuwape, A. U., and Omeike, Mathew Omonigho. "Further ultimate boundedness of solutions of some system of third order nonlinear ordinary differential equations." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 43.1 (2004): 7-20. <http://eudml.org/doc/32353>.

@article{Afuwape2004,
abstract = {In this paper, we shall give sufficient conditions for the ultimate boundedness of solutions for some system of third order non-linear ordinary differential equations of the form \[\{\mathop \{\smash\{X\}\vrule width0ptheight5.46pt\}\limits ^\{\hbox\{t\}o 8pt\{\hss \footnotesize \hspace\{1.0pt\}.\hspace\{-0.65002pt\}.\hspace\{-0.65002pt\}.\hss \}\}\}+F(\ddot\{X\})+G(\dot\{X\})+H(X)= P(t,X,\dot\{X\},\ddot\{X\})\] where $X,F(\ddot\{X\})$, $G(\dot\{X\})$, $H(X)$, $P(t,X,\dot\{X\},\ddot\{X\})$ are real $n$-vectors with $F,G$, $H:\mathbb \{R\}^n\rightarrow \mathbb \{R\}^n$ and $P:\mathbb \{R\}\times \mathbb \{R\}^n\times \mathbb \{R\}^n\times \mathbb \{R\}^n\rightarrow \mathbb \{R\}^n$ continuous in their respective arguments. We do not necessarily require that $F(\ddot\{X\}),G(\dot\{X\})$ and $H(X)$ are differentiable. Using the basic tools of a complete Lyapunov Function, earlier results are generalized.},
author = {Afuwape, A. U., Omeike, Mathew Omonigho},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {ultimate boundedness; complete Lyapunov functions; nonlinear third order system; ultimate boundedness; complete Lyapunov functions; nonlinear third-order system},
language = {eng},
number = {1},
pages = {7-20},
publisher = {Palacký University Olomouc},
title = {Further ultimate boundedness of solutions of some system of third order nonlinear ordinary differential equations},
url = {http://eudml.org/doc/32353},
volume = {43},
year = {2004},
}

TY - JOUR
AU - Afuwape, A. U.
AU - Omeike, Mathew Omonigho
TI - Further ultimate boundedness of solutions of some system of third order nonlinear ordinary differential equations
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2004
PB - Palacký University Olomouc
VL - 43
IS - 1
SP - 7
EP - 20
AB - In this paper, we shall give sufficient conditions for the ultimate boundedness of solutions for some system of third order non-linear ordinary differential equations of the form \[{\mathop {\smash{X}\vrule width0ptheight5.46pt}\limits ^{\hbox{t}o 8pt{\hss \footnotesize \hspace{1.0pt}.\hspace{-0.65002pt}.\hspace{-0.65002pt}.\hss }}}+F(\ddot{X})+G(\dot{X})+H(X)= P(t,X,\dot{X},\ddot{X})\] where $X,F(\ddot{X})$, $G(\dot{X})$, $H(X)$, $P(t,X,\dot{X},\ddot{X})$ are real $n$-vectors with $F,G$, $H:\mathbb {R}^n\rightarrow \mathbb {R}^n$ and $P:\mathbb {R}\times \mathbb {R}^n\times \mathbb {R}^n\times \mathbb {R}^n\rightarrow \mathbb {R}^n$ continuous in their respective arguments. We do not necessarily require that $F(\ddot{X}),G(\dot{X})$ and $H(X)$ are differentiable. Using the basic tools of a complete Lyapunov Function, earlier results are generalized.
LA - eng
KW - ultimate boundedness; complete Lyapunov functions; nonlinear third order system; ultimate boundedness; complete Lyapunov functions; nonlinear third-order system
UR - http://eudml.org/doc/32353
ER -

References

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  9. Ezeilo J. O. C., Tejumola H. O., Further results for a system of third order ordinary differential equations, Atti. Acad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 58 (1975), 143–151. (1975) MR0425261
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Citations in EuDML Documents

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  1. Irena Rachůnková, Jan Tomeček, Singular nonlinear problem for ordinary differential equation of the second order
  2. Mathew Omonigho Omeike, Stability and Boundedness of Solutions of a Certain System of Third-order Nonlinear Delay Differential Equations
  3. Mathew Omonigho Omeike, A. U. Afuwape, New result on the ultimate boundedness of solutions of certain third-order vector differential equations
  4. Djamila Beldjerd, Moussadek Remili, Boundedness and square integrability of solutions of certain third-order differential equations
  5. Mathew Omonigho Omeike, O. O. Oyetunde, A. L. Olutimo, Boundedness of Solutions of Certain System of Second-order Ordinary Differential Equations
  6. Larbi Fatmi, Moussadek Remili, Stability and Boundedness of Solutions of Some Third-order Nonlinear Vector Delay Differential Equation
  7. Anthony Uyi Afuwape, Mathew Omonigho Omeike, Ultimate boundedness of some third order ordinary differential equations

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