| Title:
|
Results on Non-resonant Oscillations for some Nonlinear Vector Fourth Order Differential Systems (English) |
| Author:
|
Ukpera, Awar Simon |
| Author:
|
Adesina, Olufemi Adeyinka |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
51 |
| Issue:
|
2 |
| Year:
|
2012 |
| Pages:
|
129-140 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This paper presents vector versions of some existence results recently published for certain fourth order differential systems based on generalisations drawn from possibilities arising from the underlying auxiliary equation. The results obtained also extend some known works involving third order differential systems to the corresponding fourth order. (English) |
| Keyword:
|
non-resonant oscillations |
| Keyword:
|
fourth order differential systems |
| Keyword:
|
Leray–Schauder continuation techniques |
| MSC:
|
34B15 |
| MSC:
|
34C15 |
| MSC:
|
34C25 |
| idZBL:
|
Zbl 06204935 |
| idMR:
|
MR3058878 |
| . |
| Date available:
|
2012-11-26T10:22:34Z |
| Last updated:
|
2014-03-12 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143072 |
| . |
| Reference:
|
[1] Afuwape, A. U., Omari, P., Zanolin, F.: Nonlinear perturbations of differential operators with nontrivial kernel and applications to third-order periodic boundary value problems. J. Math. Anal. Appl. 143, 1 (1989), 35–56. Zbl 0695.47044, MR 1019448, 10.1016/0022-247X(89)90027-9 |
| Reference:
|
[2] Afuwape, A. U., Ukpera, A. S.: Existence of solutions of periodic boundary value problems for some vector third order differential equations. J. Nig. Math. Soc. 20 (2001), 1–17. MR 2055195 |
| Reference:
|
[3] Ezeilo, J. O. C.: Non-resonant oscillations for some fourth order differential equations I. In: Ekhaguere, G.O.S., Ugbebor, O. (eds.): Directions in Mathematics, Associated Book Makers, Ibadan, 1999, 15–35. MR 1754542 |
| Reference:
|
[4] Ezeilo, J. O. C.: Periodic boundary value problems for some fourth order differential equations. In: Tejumola, H.O., Ezeilo, J.O.C., Afuwape, A.U. (eds.): Proceedings of National Mathematical Centre on Ordinary Differential Equations, National Mathematical Centre, Abuja, Nigeria, 1, 1 (2000), 1–14. MR 1991397 |
| Reference:
|
[5] Ezeilo, J. O. C., Nkashama, M. N.: Resonant and nonresonant oscillations for third-order nonlinear ordinary differential equations. Nonl. Anal. T.M.A. 12, 10 (1988), 1029–1046. MR 0962767, 10.1016/0362-546X(88)90098-3 |
| Reference:
|
[6] Ezeilo, J. O. C., Omari, P.: Nonresonant oscillations for some third-order Differential equations II. J. Nig. Math. Soc. 8 (1989), 25–48. |
| Reference:
|
[7] Ezeilo, J. O. C., Onyia, J.: Nonresonant oscillations for some third-order differential equations I. J. Nig. Math. Soc. 3 (1984), 83–96. MR 0852884 |
| Reference:
|
[8] Reissig, R., Sansone, G., Conti, R.: Nonlinear Differential Equations of Higher Order. Noordhoff Pub., Groningen, 1974. MR 0344556 |
| Reference:
|
[9] Tejumola, H. O.: Existence of periodic solutions for certain nonlinear fourth order differential equations. In: Animalu, A.O.E., Iyahen, S.O., Tejumola, H.O. (eds.): Contributions to the Development of Mathematics in Nigeria, National Mathematical Centre, Abuja, 2000, 41–49. |
| Reference:
|
[10] Tejumola, H. O.: Periodic boundary value problems for some fifth, fourth and third order ordinary differential equations. J. Nig. Math. Soc. 25 (2006), 37–46. MR 2376824 |
| Reference:
|
[11] Ukpera, A. S.: Periodic solutions of certain third order differential systems with nonlinear dissipation. Acta Univ. Palacki. Olomuc., Math. 41 (2002), 113–125. Zbl 1040.34049, MR 1968227 |
| Reference:
|
[12] Ukpera, A. S.: Asymptotic conditions for solving non-symmetric problems of third order nonlinear differential systems. Electron. J. Diff. Equat. 2008, 154 (2008), 1–15. Zbl 1176.34022, MR 2470951 |
| . |
