| Title:
|
Oscillation theorems for neutral differential equations with the quasi-derivatives (English) |
| Author:
|
Růžičková, M. |
| Author:
|
Špániková, E. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
30 |
| Issue:
|
4 |
| Year:
|
1994 |
| Pages:
|
293-300 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The authors study the n-th order nonlinear neutral differential equations with the quasi – derivatives $L_n[x(t)+(-1)^r P(t) x(g(t))]+\delta Q(t) f(x(h(t))) = 0,$ where $\ n \ge 2,\ r \in \lbrace 1,2\rbrace ,\ $ and $ \delta = \pm 1.$ There are given sufficient conditions for solutions to be either oscillatory or they converge to zero. (English) |
| Keyword:
|
neutral differential equation |
| Keyword:
|
oscillatory (nonoscillatory) solution |
| Keyword:
|
quasi derivatives |
| MSC:
|
34C10 |
| MSC:
|
34K15 |
| MSC:
|
34K25 |
| MSC:
|
34K40 |
| MSC:
|
34K99 |
| idZBL:
|
Zbl 0819.34046 |
| idMR:
|
MR1322574 |
| . |
| Date available:
|
2008-06-06T21:27:27Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107516 |
| . |
| Reference:
|
[1] Graef, J. R., Spikes, P. W.: On the oscillation of an $n$th-order nonlinear neutral delay differential equation.J. Comp. Appl. Math. 41 (1992), 35-40. MR 1181706 |
| Reference:
|
[2] Jaroš, J., Kusano, T.: Oscillation properties of first order nonlinear functional differential equations of neutral type.Diff. and Int. Equat. (1991), 425-436. MR 1081192 |
| Reference:
|
[3] Marušiak, P.: Oscillatory properties of functional differential systems of neutral type.Czech. Math. J. 43 (1993), 649-662. MR 1258427 |
| Reference:
|
[4] Šeda, V.: Nonoscillatory solutions of differential equations with deviating argument.Czech. Math. J. 36 (111) (1986), 93-107. MR 0822871 |
| Reference:
|
[5] Zafer, A., Dahiya, R. S.: Oscillation of bounded solutions of neutral differential equations.Appl. Math. Lett. 2 (1993), 43-46. MR 1347773 |
| . |
