Boundedness of Solutions of Certain System of Second-order Ordinary Differential Equations

Mathew Omonigho Omeike; O. O. Oyetunde; A. L. Olutimo

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2014)

  • Volume: 53, Issue: 1, page 107-115
  • ISSN: 0231-9721

Abstract

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We extend, in this paper, some known results on the boundedness of solutions of certain second order nonlinear scalar differential equations to system of second order nonlinear differential equations.

How to cite

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Omeike, Mathew Omonigho, Oyetunde, O. O., and Olutimo, A. L.. "Boundedness of Solutions of Certain System of Second-order Ordinary Differential Equations." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 53.1 (2014): 107-115. <http://eudml.org/doc/261963>.

@article{Omeike2014,
abstract = {We extend, in this paper, some known results on the boundedness of solutions of certain second order nonlinear scalar differential equations to system of second order nonlinear differential equations.},
author = {Omeike, Mathew Omonigho, Oyetunde, O. O., Olutimo, A. L.},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {boundedness; Lyapunov function; differential equations of second-order; boundedness; system; second order ordinary; differential equations},
language = {eng},
number = {1},
pages = {107-115},
publisher = {Palacký University Olomouc},
title = {Boundedness of Solutions of Certain System of Second-order Ordinary Differential Equations},
url = {http://eudml.org/doc/261963},
volume = {53},
year = {2014},
}

TY - JOUR
AU - Omeike, Mathew Omonigho
AU - Oyetunde, O. O.
AU - Olutimo, A. L.
TI - Boundedness of Solutions of Certain System of Second-order Ordinary Differential Equations
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2014
PB - Palacký University Olomouc
VL - 53
IS - 1
SP - 107
EP - 115
AB - We extend, in this paper, some known results on the boundedness of solutions of certain second order nonlinear scalar differential equations to system of second order nonlinear differential equations.
LA - eng
KW - boundedness; Lyapunov function; differential equations of second-order; boundedness; system; second order ordinary; differential equations
UR - http://eudml.org/doc/261963
ER -

References

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  1. Afuwape, A. U., 10.1016/0022-247X(83)90243-3, J. Math. Anal. Appl. 97 (1983), 140–150. (1983) MR0721235DOI10.1016/0022-247X(83)90243-3
  2. Afuwape, A. U., Further ultimate boundedness results for a third-order nonlinear system of differential equations, Analisi Funzionale e Appl. 6, 99-100, N.I. (1985), 348–360. (1985) MR0805225
  3. Afuwape, A. U., Omeike, M. O., Further ultimate boundedness of solutions of some system of third-order nonlinear ordinary differential equations, Acta Univ. Palacki. Olomuc., Fac. rer. nat., Math. 43 (2004), 7–20. (2004) MR2124598
  4. Ezeilo, J. O. C., 10.1016/0022-247X(67)90035-2, J. Math. Anal. Appl. 18 (1967), 395–416. (1967) Zbl0173.10302MR0212298DOI10.1016/0022-247X(67)90035-2
  5. Ezeilo, J. O. C., 10.1007/BF02414336, Ann. Math. Pura Appl. 72, 4 (1966), 239–252. (1966) MR0203144DOI10.1007/BF02414336
  6. Ezeilo, J. O. C., 10.1007/BF02412444, Ann. Math. Pura Appl. 66, 4 (1964), 233–250. (1964) Zbl0126.30403MR0173831DOI10.1007/BF02412444
  7. Ezeilo, J. O. C., Tejumola, H. O., 10.1007/BF02416460, Ann. Math. Pura Appl. 74 (1966), 283–316. (1966) MR0204787DOI10.1007/BF02416460
  8. Ezeilo, J. O. C., Tejumola, H. O., Further results for a system of third-order ordinary differential equations, Atti. Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 58 (1975), 143–151. (1975) MR0425261
  9. Meng, F. W., 10.1006/jmaa.1993.1273, J. Math. Anal. Appl. 177 (1993), 496–509. (1993) MR1231497DOI10.1006/jmaa.1993.1273
  10. Rao, M. R. M., Ordinary differential equations, Affiliated East-West Private Limited, London, 1980. (1980) Zbl0482.34001
  11. Reissig, R., Sansone, G., Conti, R., Nonlinear Differential Equations of Higher Order, Noordhoff, Groningen, 1974. (1974) 
  12. Tejumola, H. O., 10.1007/BF02411167, Ann. Math. Pura Appl. 83, 4 (1969), 195–212. (1969) MR0262597DOI10.1007/BF02411167
  13. Tejumola, H. O., Boundedness criteria for solutions of some second order differential equations, Academia Nazionale Dei Lincei, Serie VII, 50, 4 (1971), 204–209. (1971) Zbl0235.34081MR0306619
  14. Tejumola, H. O., On a Lienard type matrix differential equation, Atti. Accad. Naz. Lincei Rendi. Cl. Sci. Fis. Mat. Natur (8) 60, 2 (1976), 100–107. (1976) Zbl0374.34035MR0473341
  15. Tiryaki, A., Boundedness and periodicity results for a certain system of third-order nonlinear differential equations, Indian J. Pure Appl. Math. 30, 4 (1999), 361–372. (1999) Zbl0936.34041MR1695688
  16. Tunc, C., 10.1016/j.na.2008.03.002, Nonlinear Analysis 70, 6 (2009), 2232–2236. (2009) Zbl1162.34043MR2498299DOI10.1016/j.na.2008.03.002
  17. Yoshizawa, T., On the evaluation of the derivatives of solutions of y ' ' = f ( x , y , y ' ) , Mem. Coll. Sci., Univ. Kyoto, Series A, Math. 28 (1953), 27–32, 133–141. (1953) MR0060088

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