| Title:
|
On oscillation of solutions of forced nonlinear neutral differential equations of higher order (English) |
| Author:
|
Parhi, N. |
| Author:
|
Rath, R. N. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
53 |
| Issue:
|
4 |
| Year:
|
2003 |
| Pages:
|
805-825 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, necessary and sufficient conditions are obtained for every bounded solution of \[ [y (t) - p (t) y (t - \tau )]^{(n)} + Q (t) G \bigl (y (t - \sigma )\bigr ) = f (t), \quad t \ge 0, \qquad \mathrm{(*)}\] to oscillate or tend to zero as $t \rightarrow \infty $ for different ranges of $p (t)$. It is shown, under some stronger conditions, that every solution of $(*)$ oscillates or tends to zero as $t \rightarrow \infty $. Our results hold for linear, a class of superlinear and other nonlinear equations and answer a conjecture by Ladas and Sficas, Austral. Math. Soc. Ser. B 27 (1986), 502–511, and generalize some known results. (English) |
| Keyword:
|
oscillation |
| Keyword:
|
nonoscillation |
| Keyword:
|
neutral equations |
| Keyword:
|
asymptotic behaviour |
| MSC:
|
34C10 |
| MSC:
|
34C15 |
| MSC:
|
34K11 |
| MSC:
|
34K25 |
| MSC:
|
34K40 |
| idZBL:
|
Zbl 1080.34522 |
| idMR:
|
MR2018832 |
| . |
| Date available:
|
2009-09-24T11:06:52Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127842 |
| . |
| Reference:
|
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| Reference:
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