Results on Non-resonant Oscillations for some Nonlinear Vector Fourth Order Differential Systems

Awar Simon Ukpera; Olufemi Adeyinka Adesina

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2012)

  • Volume: 51, Issue: 2, page 129-140
  • ISSN: 0231-9721

Abstract

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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.

How to cite

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Ukpera, Awar Simon, and Adesina, Olufemi Adeyinka. "Results on Non-resonant Oscillations for some Nonlinear Vector Fourth Order Differential Systems." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 51.2 (2012): 129-140. <http://eudml.org/doc/246657>.

@article{Ukpera2012,
abstract = {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.},
author = {Ukpera, Awar Simon, Adesina, Olufemi Adeyinka},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {non-resonant oscillations; fourth order differential systems; Leray–Schauder continuation techniques; non-resonant oscillations; fourth-order differential systems; Leray-Schauder continuation techniques},
language = {eng},
number = {2},
pages = {129-140},
publisher = {Palacký University Olomouc},
title = {Results on Non-resonant Oscillations for some Nonlinear Vector Fourth Order Differential Systems},
url = {http://eudml.org/doc/246657},
volume = {51},
year = {2012},
}

TY - JOUR
AU - Ukpera, Awar Simon
AU - Adesina, Olufemi Adeyinka
TI - Results on Non-resonant Oscillations for some Nonlinear Vector Fourth Order Differential Systems
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2012
PB - Palacký University Olomouc
VL - 51
IS - 2
SP - 129
EP - 140
AB - 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.
LA - eng
KW - non-resonant oscillations; fourth order differential systems; Leray–Schauder continuation techniques; non-resonant oscillations; fourth-order differential systems; Leray-Schauder continuation techniques
UR - http://eudml.org/doc/246657
ER -

References

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  1. Afuwape, A. U., Omari, P., Zanolin, F., 10.1016/0022-247X(89)90027-9, J. Math. Anal. Appl. 143, 1 (1989), 35–56. (1989) Zbl0695.47044MR1019448DOI10.1016/0022-247X(89)90027-9
  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. (2001) MR2055195
  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. (1999) MR1754542
  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. (2000) MR1991397
  5. Ezeilo, J. O. C., Nkashama, M. N., 10.1016/0362-546X(88)90098-3, Nonl. Anal. T.M.A. 12, 10 (1988), 1029–1046. (1988) MR0962767DOI10.1016/0362-546X(88)90098-3
  6. Ezeilo, J. O. C., Omari, P., Nonresonant oscillations for some third-order Differential equations II, J. Nig. Math. Soc. 8 (1989), 25–48. (1989) 
  7. Ezeilo, J. O. C., Onyia, J., Nonresonant oscillations for some third-order differential equations I, J. Nig. Math. Soc. 3 (1984), 83–96. (1984) MR0852884
  8. Reissig, R., Sansone, G., Conti, R., Nonlinear Differential Equations of Higher Order, Noordhoff Pub., Groningen, 1974. (1974) MR0344556
  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. (2000) 
  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. (2006) MR2376824
  11. Ukpera, A. S., Periodic solutions of certain third order differential systems with nonlinear dissipation, Acta Univ. Palacki. Olomuc., Math. 41 (2002), 113–125. (2002) Zbl1040.34049MR1968227
  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. (2008) Zbl1176.34022MR2470951

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