| Title:
|
Periodicity and stability results for solutions of some fifth order nonlinear differential equations (English) |
| Author:
|
Adesina, Olufemi Adeyinka |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
40 |
| Issue:
|
1 |
| Year:
|
2001 |
| Pages:
|
7-16 |
| . |
| Category:
|
math |
| . |
| MSC:
|
34C25 |
| MSC:
|
34D20 |
| idZBL:
|
Zbl 1040.34060 |
| idMR:
|
MR1904678 |
| . |
| Date available:
|
2009-01-29T15:57:27Z |
| Last updated:
|
2012-05-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/120422 |
| . |
| Reference:
|
[1] Abou-El-Ela A. M. A., Sadek A. I.: On the boundedness of a certain system of fifth-order differential equation.Annals of Diff. Eqs. 14, 1 (1998), 1-10. MR 1633652 |
| Reference:
|
[2] Afuwape A. U.: Solutions of some third-order non-linear differential equations: Frequency-domain method.An. sti. Univ. Al. I. Cuza, Iasi sect. 1.a, Mat. T. XXV (1979), 297-302. Zbl 0426.34044, MR 0562315 |
| Reference:
|
[3] Afuwape A. U.: Conditions on the behaviour of solutions for a certain class of third-order non-linear differential equations.An. sti. Univ. Al. I. Cuza, Iasi sect. Iasi 30 (1979), 30-34. MR 0777023 |
| Reference:
|
[4] Afuwape A. U.: On some properties of solutions for certain fourth-order non-linear differential equations.Analysis 5 (1985) 175-183. MR 0791498 |
| Reference:
|
[5] Afuwape A. U.: Frequency-domain approach to non-linear oscillations of some third-order differential equations.Nonlinear Analysis, Theory, Methods and Applications 10, 12 (1986), 1459-1470. MR 0869553 |
| Reference:
|
[6] Afuwape A. U., Adesina O. A.: Conditions on the qualitative behaviour of solutions for a certain class of fifth-order nonlinear differential equations.Ann. Stii. Univ. Al. I. Cuza, Iasi. Mat. T. XLVI, f. 2 (2000), (In Press). Zbl 1009.34043, MR 1991403 |
| Reference:
|
[7] Barbalat I., Halanay A.: Applications of the frequency-domain method to forced non-linear oscillations.Math. Nachr. 44 (1970), 165-179. MR 0269934 |
| Reference:
|
[8] Barbalat I., Halanay A.: Conditions de comportment "Presque lineaire" dan la theorie des oscillations.Rev. Roum. Sci. Techn. Electrote chn. Energ. 29 (1974), 321-341. MR 0352613 |
| Reference:
|
[9] Barbalat I.: Conditions pour un bon comportment de certaines equations differentielles du troisieme et du quatrieme ordre.Equations differentielles et fonctionnelles non-lineaires (Eds: P. Janssens, J. Mawhin, N. Rouche), Hermann, Paris, 1973, 80-91. MR 0402211 |
| Reference:
|
[10] Chukwu E. N.: On the boundedness and stability of solutions of some differential equations of the fifth order.SIAM Math. Anal. 7, 2 (1976), 176-194. Zbl 0346.34038, MR 0425274 |
| Reference:
|
[11] Kalman R. E.: Lyapunov functions for the problem of Lurie in automatic control.Proc. Natn. Acad. Sci. U.S.A. 49 (1963), 201-205. MR 0151696 |
| Reference:
|
[12] Popov V. M.: Absolute stability of non-linear control systems.Aut. Rem. Control 22 (1962), 867-875. |
| Reference:
|
[13] Reissig R., Sansone G., Conti R.: Non-linear differential equations of higher order.Noordhoff, Groninger, 1974. Zbl 0275.34001, MR 0344556 |
| Reference:
|
[14] Rouche N., Habets P., Laloy M.: Stability theory by Liapunov’s direct method.Springer Verlag, New York, Heidelberg, Berlin, 1977. Zbl 0364.34022, MR 0450715 |
| Reference:
|
[15] Tejumola H. O.: Further remarks on the existence of periodic solutions of certain fifth-order non-linear differential equation.Atti Accad. Naz. Dei Lincei, ser VIII, 53, fasc. 3 (1975), 323-327. MR 0425262 |
| Reference:
|
[16] Yacubovich V. A.: Solutions of some matrix inequalities occuring in the theory of automatic control.Soviet Math. Dokl. 4 (1962), 1304-1307. |
| Reference:
|
[17] Yacubovich V. A.: The matrix method in the theory of the stability of non-linear control systems.Aut. Rem. Control 25 (1964), 905-916. |
| Reference:
|
[18] Yacubovich V. A.: Frequency-domain conditions for absolute stability and dissipativity of control systems with one differentiable non-linearity.Soviet Math. Dokl. 6 (1965), 81-101. |
| Reference:
|
[19] Yacubovich V. A.: Periodic and almost periodic limit states of controlled systems with several, in general discotinuous non-linearities.Soviet Math. Dokl. 7 (1966), 1517-1521. |
| . |
