| Title:
|
Oscillatory behaviour of solutions of nonlinear higher order neutral differential equations (English) |
| Author:
|
Parhi, N. |
| Author:
|
Rath, R. N. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
129 |
| Issue:
|
1 |
| Year:
|
2004 |
| Pages:
|
11-27 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Necessary and sufficient conditions are obtained for oscillation of all bounded solutions of \[ [y(t) - y(t-\tau )]^{(n)} + Q(t) G(y(t-\sigma )) = 0, \ t \ge 0, \tag $*$ \] where $n \ge 3$ is odd. Sufficient conditions are obtained for all solutions of $(*)$ to oscillate. Further, sufficient conditions are given for all solutions of the forced equation associated with $(*)$ to oscillate or tend to zero as $t \rightarrow \infty $. In this case, there is no restriction on $n$. (English) |
| Keyword:
|
oscillation |
| Keyword:
|
nonoscillation |
| Keyword:
|
neutral differential equations |
| MSC:
|
34C10 |
| MSC:
|
34C15 |
| MSC:
|
34K11 |
| MSC:
|
34K40 |
| idZBL:
|
Zbl 1069.34093 |
| idMR:
|
MR2048783 |
| DOI:
|
10.21136/MB.2004.134104 |
| . |
| Date available:
|
2009-09-24T22:12:05Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134104 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[3] Q. Chuanxi et al: Sufficient conditions for oscillation and existence of positive solutions.Appl. Anal. 35 (1990), 187–194. Zbl 0709.34055, MR 1387408, 10.1080/00036819008839916 |
| Reference:
|
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| Reference:
|
[5] Pitambar Das: Oscillation criteria for odd order neutral equations.J. Math. Anal. Appl. 188 (1994), 245–257. MR 1301730, 10.1006/jmaa.1994.1425 |
| Reference:
|
[6] I. Gyori, G. Ladas: Oscillation Theory of Delay-Differential Equations.Clarendon Press, Oxford, 1991. MR 1168471 |
| Reference:
|
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| Reference:
|
[8] N. Parhi, R. N. Rath: On oscillation and asymptotic behaviour of solutions of forced first order neutral differential equations.Proc. Indian Acad. Sci. (Math. Sci.) 3 (2001), 337–350. MR 1851095 |
| Reference:
|
[9] N. Parhi, R. N. Rath: On oscillation of solutions of forced nonlinear neutral differential equations of higher order.Czechoslovak Math. J. 53 (2003), 805–825. MR 2018832, 10.1007/s10587-004-0805-8 |
| Reference:
|
[10] N. Parhi, R. N. Rath: On oscillation of solutions of forced nonlinear neutral differential equations of higher order II.Ann. Pol. Math. 81 (2003), 101–110. MR 1976190, 10.4064/ap81-2-1 |
| . |
