Stability and boundedness of solutions of nonlinear vector differential equations of third order
Archivum Mathematicum (2014)
- Volume: 050, Issue: 2, page 101-106
- ISSN: 0044-8753
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topOmeike, Mathew Omonigho. "Stability and boundedness of solutions of nonlinear vector differential equations of third order." Archivum Mathematicum 050.2 (2014): 101-106. <http://eudml.org/doc/261176>.
@article{Omeike2014,
abstract = {The paper studies the equation
\begin\{equation*\}\dddot\{X\}+\Psi (\dot\{X\})\ddot\{X\}+\Phi (X)\dot\{X\}+cX=P(t) \end\{equation*\}
in two cases:
(i) $P(t)\equiv 0$,
(ii) $P(t)\ne 0$.
In case (i), the global asymptotic stability of the solution $X=0$ is studied; in case (ii), the boundedness of all solutions is proved.},
author = {Omeike, Mathew Omonigho},
journal = {Archivum Mathematicum},
keywords = {boundedness; stability; Liapunov function; differential equations of third order; boundedness; stability; Liapunov function; differential equations of third order},
language = {eng},
number = {2},
pages = {101-106},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Stability and boundedness of solutions of nonlinear vector differential equations of third order},
url = {http://eudml.org/doc/261176},
volume = {050},
year = {2014},
}
TY - JOUR
AU - Omeike, Mathew Omonigho
TI - Stability and boundedness of solutions of nonlinear vector differential equations of third order
JO - Archivum Mathematicum
PY - 2014
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 050
IS - 2
SP - 101
EP - 106
AB - The paper studies the equation
\begin{equation*}\dddot{X}+\Psi (\dot{X})\ddot{X}+\Phi (X)\dot{X}+cX=P(t) \end{equation*}
in two cases:
(i) $P(t)\equiv 0$,
(ii) $P(t)\ne 0$.
In case (i), the global asymptotic stability of the solution $X=0$ is studied; in case (ii), the boundedness of all solutions is proved.
LA - eng
KW - boundedness; stability; Liapunov function; differential equations of third order; boundedness; stability; Liapunov function; differential equations of third order
UR - http://eudml.org/doc/261176
ER -
References
top- Chukwu, E.N., On boundedness of solutions of third ordr differential equations, Ann. Math. Pura Appl. (4) 104 (1975), 123–149. (1975) MR0377180
- Ezeilo, J.O.C., A generalization of a boundedness theorem for a certain third-order differential equation, Proc. Cambridge Philos. Soc. 63 (1967), 735–742. (1967) MR0213657
- Liapunov, A.M., Stability of Motion, Academic Press London, 1906. (1906) MR0208093
- Mehri, B., Shadman, D., Boundedness of solutions of certain third order differential equations, Math. Inequal. Appl. 2 (1999), no. 4, 545–549. (1999) MR1717047
- Omeike, M.O., Afuwape, A.U., New result on the ultimate boundedness of solutions of certain third-order vector differential equations, Acta Univ. Palack. Olomuc. Fac. Rerum Natur. Math. 49 (2010), no. 1, 55–61. (2010) MR2797523
- Rao, M.R.M., Ordinary Differential Equations, Affiliated East West Private Limited, London, 1980. (1980) Zbl0482.34001
- Reissig, R., Sansone, G., Conti, R., Nonlinear Differential Equations of Higher Order, Noordhoff Groningen, 1974. (1974)
- Tejumola, H.O., 10.1007/BF02417936, Ann. Mat. Pura Appl. (4) 92 (1972), no. 4, 65–75. (1972) Zbl0242.34046MR0318615DOI10.1007/BF02417936
- Tunc, C., Uniform ultimate boundedness of the solutions of third order nonlinear differential equations, Kuwait J. Sci. Engrg. 12 (2005), no. 1, 39–48. (2005) Zbl1207.34043MR2145249
- Tunc, C., 10.1016/j.na.2008.03.002, Nonlinear Anal. 70 (2009), 2232–2236. (2009) Zbl1162.34043MR2498299DOI10.1016/j.na.2008.03.002
- Tunc, C., Ates, M., Stability and boundedness results for solutions of certain third order nonlinear vector differential equations, Nonlinear Dynam. 45 (2006), no. 3–4, 271–281. (2006) Zbl1132.34328MR2250136
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