| Title:
|
Further results for some third order differential systems with nonlinear dissipation (English) |
| Author:
|
Ukpera, Awar Simon |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
43 |
| Issue:
|
1 |
| Year:
|
2004 |
| Pages:
|
155-169 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
nonlinear dissipation |
| Keyword:
|
sharp and nonuniform nonresonance |
| MSC:
|
34B15 |
| MSC:
|
34C15 |
| MSC:
|
34C25 |
| idZBL:
|
Zbl 1076.34050 |
| idMR:
|
MR2124614 |
| . |
| Date available:
|
2009-08-21T12:55:21Z |
| Last updated:
|
2012-05-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/132951 |
| . |
| 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 |
| Reference:
|
[2] Andres J., Vlček V.: Periodic solutions of the third order parametric differential equations involving large nonlinearities.Math. Slovaca 41, 4 (1991), 337–349. Zbl 0753.34025, MR 1149042 |
| Reference:
|
[3] Conti G., Iannacci R., Nkashama M. N.: Periodic solutions of Liénard systems at resonance.Ann. Math. Pura. Appl. 141, 4 (1985), 313–327. Zbl 0577.34035, MR 0798178 |
| Reference:
|
[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. MR 0962767 |
| Reference:
|
[5] Ezeilo J. O. C., Omari P.: Nonresonant oscillations for some third-order Differential equations II.J. Nigerian Math. Soc. 8 (1989), 25–48. |
| Reference:
|
[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. Zbl 0414.34025, MR 0525202 |
| Reference:
|
[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. Zbl 0536.34022, MR 0683859 |
| Reference:
|
[8] Mawhin J., Ward J. R.: Periodic solutions of some forced Liénard differential equations at resonance.Arch. Math. 41 (1983), 337–351. Zbl 0537.34037, MR 0731606 |
| Reference:
|
[9] Minhós F.: Periodic solutions for a third order differential equation under conditions on the potential.Portugaliae Math. 55, 4 (1998), 475–484. Zbl 0923.34045, MR 1672255 |
| Reference:
|
[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). |
| Reference:
|
[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. Zbl 1009.34013, MR 1880207 |
| Reference:
|
[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. Zbl 1040.34049, MR 1968227 |
| . |
