| Title:
|
Some stability and boundedness results for the solutions of certain fourth order differential equations (English) |
| Author:
|
Tunç, Cemil |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
44 |
| Issue:
|
1 |
| Year:
|
2005 |
| Pages:
|
161-171 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Sufficient conditions are established for the asymptotic stability of the zero solution of the equation (1.1) with $p\equiv 0$ and the boundedness of all solutions of the equation (1.1) with $p\ne 0$. Our result includes and improves several results in the literature ([4], [5], [8]). (English) |
| Keyword:
|
differential equations of fourth order |
| Keyword:
|
boundedness |
| Keyword:
|
stability |
| Keyword:
|
Lyapunov functions |
| MSC:
|
34C11 |
| MSC:
|
34D20 |
| MSC:
|
34D99 |
| idZBL:
|
Zbl 1095.34536 |
| idMR:
|
MR2218575 |
| . |
| Date available:
|
2009-08-21T06:51:01Z |
| Last updated:
|
2012-05-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133385 |
| . |
| Reference:
|
[1] Barbashin E. A.: Liapunov’s Function. : Science., 1970. |
| Reference:
|
[2] Chukwu E. N.: On the boundedness of a certain fourth-order differential equation.J. London Math. Soc. (2) 11, 3 (1975), 313–324. MR 0390396 |
| Reference:
|
[3] Ezeilo J. O. C. , Tejumola H. O.: On the boundedness and the stability properties of solutions of certain fourth order differential equation.Ann. Mat. Pure. Apl. (IV) 95 (1973), 131–145. MR 0425275 |
| Reference:
|
[4] Hu C. Y.: The stability in the large for certain fourth order differential equations.Ann. Differential Equations 8, 4 (1992), 422–428. Zbl 0776.34040, MR 1215987 |
| Reference:
|
[5] Ponzo P. J.: On the stability of certain nonlinear differential equations.IEEE Trans. Automatic Control 10 (1965), 470–472. MR 0188554 |
| Reference:
|
[6] Reissig R., Sansone G., Conti R.: Nonlinear Differential Equations of Higher Order. : Noordhoff, Groningen., 1974. |
| Reference:
|
[7] Tunç C.: A note on the stability and boundedness results of solutions of certain fourth order differential equations.Appl. Math. Comp. 155, 3 (2004), 837–843. MR 2078694 |
| Reference:
|
[8] Wu X., Xiong K.: Remarks on stability results for the solutions of certain fourth-order autonomous differential equations.Internat. J. Control. 69, 2 (1998), 353–360. Zbl 0934.34039, MR 1684744 |
| . |
