| Title:
|
Further results on global stability of solutions of certain third-order nonlinear differential equations (English) |
| Author:
|
Omeike, Mathew Omonigho |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
47 |
| Issue:
|
1 |
| Year:
|
2008 |
| Pages:
|
121-127 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Sufficient conditions are established for the global stability of solutions of certain third-order nonlinear differential equations. Our result improves on Tunc’s [10]. (English) |
| Keyword:
|
nonlinear differential equation |
| Keyword:
|
trivial solution |
| Keyword:
|
global stability |
| Keyword:
|
Lyapunov’s method |
| MSC:
|
34D23 |
| idZBL:
|
Zbl 1177.34072 |
| idMR:
|
MR2482722 |
| . |
| Date available:
|
2009-08-27T11:26:57Z |
| Last updated:
|
2012-05-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133396 |
| . |
| Reference:
|
[1] Barbashin E. A.: Lyapunov Functions. : Nauka, Moscow., 1970. |
| Reference:
|
[2] Ezeilo J. O. C.: On the stability of solutions of certain differential equations of the third order.Quart. J. Math. Oxford Ser. 11 (1960), 64–69. Zbl 0090.06603, MR 0117394 |
| Reference:
|
[3] Goldwyn M., Narendra S.: Stability of Certain Nonlinear Differential Equation Using the Second Method of Lyapunov. : Craft Lab. Harvard Univ., Cambridge, MA., 1963, pp. 1–14. |
| Reference:
|
[4] Kraovkii N. N.: Stability of Motion. : Stanford University Press, Stanford, CA., 1963. |
| Reference:
|
[5] Ogurtsov A. I.: On the stability of the solutions of some nonlinear differential equations of the third and forth order.Ivz. Vyssh. Uchebn. Zaved. Mat. 10 (1959), 200–209. |
| Reference:
|
[6] Qin Y., Wan M., Wang L.: Theory, Applications of Stability of Motions. : Academic Press, Beijing., 1981. MR 0701397 |
| Reference:
|
[7] Qian C.: On global stability of third-order nonlinear differential equations.Nonlinear Analysis 42 (2000), 651–661. Zbl 0969.34048, MR 1776296 |
| Reference:
|
[8] Qian C.: Asymptotic behavior of a third-order nonlinear differential equation.J. Math. Anal. Appl. 284 (2003), 191–205. Zbl 1054.34078, MR 1996127 |
| Reference:
|
[9] Omeike M. O.: Further results on global stability of third-order nonlinear differential equations.Nonlinear Analysis 67 (2007) 3394–3400. Zbl 1129.34323, MR 2350895 |
| Reference:
|
[10] Tunc C.: Global stability of solutions of certain third-order nonlinear differential equations.Panamer. Math. J. 14, 4 (2004), 31–35. Zbl 1065.34047, MR 2102487 |
| Reference:
|
[11] Tunc C.: On the asymptotic behavior of solutions of certain third-order nonlinear differential equations.J. Appl. Math. Stoch. Anal. 1 (2005), 29–35. Zbl 1077.34052, MR 2140325 |
| Reference:
|
[12] Reissig, R, Sansone G., Conti R.: Nonlinear Differential Equations of Higher Order. : Noordhoff Inter. Pub., Leyden., 1974. MR 0344556 |
| Reference:
|
[13] Shimanov S. N.: On the stability of the solution of a nonlinear equation of the third order.Prikl. Mat. Mekh. 17 (1953), 369–372. MR 0055523 |
| Reference:
|
[14] Wang L., Wang M.: Analysis of construction of Lyapunov functions of third-order nonlinear systems.Acta Math. Appl. Sin. 6 (1983), 309–323. MR 0748533 |
| . |
