| Title:
|
Oscillation of solutions of non-linear neutral delay differential equations of higher order for $p(t)=\pm 1$ (English) |
| Author:
|
Rath, R. N. |
| Author:
|
Padhy, L. N. |
| Author:
|
Misra, N. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
40 |
| Issue:
|
4 |
| Year:
|
2004 |
| Pages:
|
359-366 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, the oscillation criteria for solutions of the neutral delay differential equation (NDDE) \[ \left( {y(t)-p(t)\, y({t-\tau } )} \right)^{(n )}+ \alpha \,Q(t)\,\,G\left( {y({t-\sigma })} \right)= f(t) \] has been studied where $p(t) = 1$ or $p(t) \le 0$, $\alpha =\pm 1$, $Q\in C \left([0, \infty ), R^{+}\right)$, $f \in C([0, \infty ), R)$, $G \in C(R, R)$. This work improves and generalizes some recent results and answer some questions that are raised in [1]. (English) |
| Keyword:
|
oscillation |
| Keyword:
|
non-oscillation |
| Keyword:
|
neutral equations |
| Keyword:
|
asymptotic-behaviour |
| MSC:
|
34K11 |
| MSC:
|
34K40 |
| idZBL:
|
Zbl 1116.34332 |
| idMR:
|
MR2129958 |
| . |
| Date available:
|
2008-06-06T22:44:23Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107920 |
| . |
| Reference:
|
[1] Gyori I., Ladas G.: Oscillation Theory of Delay Differential Equations with Applications.Clarendon Press, Oxford, 1991. MR 1168471 |
| Reference:
|
[2] Hilderbrandt T. H.: Introduction to the Theory of Integration.Academic Press, New York, 1963. MR 0154957 |
| Reference:
|
[3] Ladde G. S., Lakshmikantham V., Zhang B. G.: Oscillation Theory of Differential Equations with Deviating Arguments.Marcel Dekker INC, New York, 1987. Zbl 0832.34071, MR 1017244 |
| Reference:
|
[4] Liu X. Z., al: Oscillation and non-oscillation for a class of neutral differential equations.Differential Equations Dynam. Systems 1 (1993), 197–204. MR 1258897 |
| Reference:
|
[5] Malik S. C., Arora S.: Mathematical Analysis.New Age International (p) Ltd. Publishers New Delhi, 2001. |
| Reference:
|
[6] Parhi N., Rath R. N.: On oscillation and asymptotic behaviour of solutions of forced first order neutral differential equations.Proc. Indian Acad. Sci. (Math. Sci.) 111 (2001), 337–350. Zbl 0995.34058, MR 1851095 |
| Reference:
|
[7] Parhi N., Rath R. N.: On oscillation of solutions of forced non-linear neutral differential equations of higher order – II.Ann. Polon. Math. 81 (2003), 101–110. MR 1976190 |
| Reference:
|
[8] Parhi N., Rath R. N.: Oscillatory behaviour of solutions of non-linear higher order neutral differential equations.Math. Bohem. 129 (2004), 11–27. MR 2048783 |
| Reference:
|
[9] Rath R. N.: Oscillatory and asymptotic behaviour of solutions of higher order neutral equations.Bull. Inst. Math. Acad. Sinica 30 (2003), 219–228. MR 1922656 |
| Reference:
|
[10] Yu J. S., al: Oscillation of neutral delay differential equation.Bull. Austral. Math. Soc. 45 (1992), 195–200. |
| . |
