Further results for some third order differential systems with nonlinear dissipation

Awar Simon Ukpera

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2004)

  • Volume: 43, Issue: 1, page 155-169
  • ISSN: 0231-9721

Abstract

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We formulate nonuniform nonresonance criteria for certain third order differential systems of the form X ' ' ' + A X ' ' + G ( t , X ' ) + C X = P ( t ) , which further improves upon our recent results in [12], given under sharp nonresonance considerations. The work also provides extensions and generalisations to the results of Ezeilo and Omari [5], and Minhós [9] from the scalar to the vector situations.

How to cite

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Ukpera, Awar Simon. "Further results for some third order differential systems with nonlinear dissipation." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 43.1 (2004): 155-169. <http://eudml.org/doc/32361>.

@article{Ukpera2004,
abstract = {We formulate nonuniform nonresonance criteria for certain third order differential systems of the form $X^\{^\{\prime \prime \prime \}\} + AX^\{^\{\prime \prime \}\} + G(t,X^\{^\{\prime \}\} ) + CX = P(t)$, which further improves upon our recent results in [12], given under sharp nonresonance considerations. The work also provides extensions and generalisations to the results of Ezeilo and Omari [5], and Minhós [9] from the scalar to the vector situations.},
author = {Ukpera, Awar Simon},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {nonlinear dissipation; sharp and nonuniform nonresonance; nonlinear dissipation; nonuniform nonresonance},
language = {eng},
number = {1},
pages = {155-169},
publisher = {Palacký University Olomouc},
title = {Further results for some third order differential systems with nonlinear dissipation},
url = {http://eudml.org/doc/32361},
volume = {43},
year = {2004},
}

TY - JOUR
AU - Ukpera, Awar Simon
TI - Further results for some third order differential systems with nonlinear dissipation
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2004
PB - Palacký University Olomouc
VL - 43
IS - 1
SP - 155
EP - 169
AB - We formulate nonuniform nonresonance criteria for certain third order differential systems of the form $X^{^{\prime \prime \prime }} + AX^{^{\prime \prime }} + G(t,X^{^{\prime }} ) + CX = P(t)$, which further improves upon our recent results in [12], given under sharp nonresonance considerations. The work also provides extensions and generalisations to the results of Ezeilo and Omari [5], and Minhós [9] from the scalar to the vector situations.
LA - eng
KW - nonlinear dissipation; sharp and nonuniform nonresonance; nonlinear dissipation; nonuniform nonresonance
UR - http://eudml.org/doc/32361
ER -

References

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  2. Andres J., Vlček V., Periodic solutions of the third order parametric differential equations involving large nonlinearities, Math. Slovaca 41, 4 (1991), 337–349. (1991) Zbl0753.34025MR1149042
  3. Conti G., Iannacci R., Nkashama M. N., Periodic solutions of Liénard systems at resonance, Ann. Math. Pura. Appl. 141, 4 (1985), 313–327. (1985) Zbl0577.34035MR0798178
  4. Ezeilo J. O. C., Nkashama M. N., Resonant and nonresonant oscillations for third-order nonlinear ordinary differential equations, Nonlinear Analysis, T.M.A. 12, 10 (1988), 1029–1046. (1988) MR0962767
  5. Ezeilo J. O. C., Omari P., Nonresonant oscillations for some third-order Differential equations II, J. Nigerian Math. Soc. 8 (1989), 25–48. (1989) 
  6. Mawhin J., Topological Degree Methods in Nonlinear Boundary Value Problems, In: CBMS Regional Conference Series in Mathematics 40 (1979), American Math. Soc., Providence, R.I. (1979) Zbl0414.34025MR0525202
  7. Mawhin J., Ward J. R., Nonuniform nonresonance conditions at the two first eigenvalues for periodic solutions of forced Liénard and Duffing equations, Rocky Mount. J. Math. 12, 4 (1982), 643–653. (1982) Zbl0536.34022MR0683859
  8. Mawhin J., Ward J. R., Periodic solutions of some forced Liénard differential equations at resonance, Arch. Math. 41 (1983), 337–351. (1983) Zbl0537.34037MR0731606
  9. Minhós F., Periodic solutions for a third order differential equation under conditions on the potential, Portugaliae Math. 55, 4 (1998), 475–484. (1998) Zbl0923.34045MR1672255
  10. Tejumola H. O., Afuwape A. U., Periodic solutions of certain third-order nonlinear differential systems with delay, I.C.T.P. Trieste, Preprint IC/90/418, (1990). (1990) 
  11. Ukpera A.S., Periodicity results for strongly nonlinear systems of third order boundary value problems, Anal. Stiint. ale Univ. “Al. I. Cuza" 46 (2000), 215–230. Zbl1009.34013MR1880207
  12. Ukpera A.S., Periodic solutions of certain third order differential systems with nonlinear dissipation, Acta Univ. Palacki. Olomuc., Fac. rer. nat., Math. 41 (2002), 147–159. Zbl1040.34049MR1968227

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