| Title:
|
Stability and boundedness of solutions of nonlinear vector differential equations of third order (English) |
| Author:
|
Omeike, M. O. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
50 |
| Issue:
|
2 |
| Year:
|
2014 |
| Pages:
|
101-106 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
boundedness |
| Keyword:
|
stability |
| Keyword:
|
Liapunov function |
| Keyword:
|
differential equations of third order |
| MSC:
|
34C11 |
| MSC:
|
34D05 |
| MSC:
|
34D20 |
| MSC:
|
34D40 |
| idZBL:
|
Zbl 06391569 |
| idMR:
|
MR3215283 |
| DOI:
|
10.5817/AM2014-2-101 |
| . |
| Date available:
|
2014-05-23T09:34:12Z |
| Last updated:
|
2015-03-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143783 |
| . |
| Reference:
|
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| Reference:
|
[2] 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. MR 0213657 |
| Reference:
|
[3] Liapunov, A.M.: Stability of Motion.Academic Press London, 1906. MR 0208093 |
| Reference:
|
[4] Mehri, B., Shadman, D.: Boundedness of solutions of certain third order differential equations.Math. Inequal. Appl. 2 (1999), no. 4, 545–549. MR 1717047 |
| Reference:
|
[5] 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. MR 2797523 |
| Reference:
|
[6] Rao, M.R.M.: Ordinary Differential Equations.Affiliated East West Private Limited, London, 1980. Zbl 0482.34001 |
| Reference:
|
[7] Reissig, R., Sansone, G., Conti, R.: Nonlinear Differential Equations of Higher Order.Noordhoff Groningen, 1974. |
| Reference:
|
[8] Tejumola, H.O.: A note on the boundedness and the stability of solutions of certain third order differential equations.Ann. Mat. Pura Appl. (4) 92 (1972), no. 4, 65–75. Zbl 0242.34046, MR 0318615, 10.1007/BF02417936 |
| Reference:
|
[9] Tunc, C.: Uniform ultimate boundedness of the solutions of third order nonlinear differential equations.Kuwait J. Sci. Engrg. 12 (2005), no. 1, 39–48. Zbl 1207.34043, MR 2145249 |
| Reference:
|
[10] Tunc, C.: On the stability and boundedness of solutions of nonlinear vector differential equations of third-order.Nonlinear Anal. 70 (2009), 2232–2236. Zbl 1162.34043, MR 2498299, 10.1016/j.na.2008.03.002 |
| Reference:
|
[11] 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. Zbl 1132.34328, MR 2250136 |
| . |
