| Title:
|
Oscillations of certain functional differential equations (English) |
| Author:
|
Grace, S. R. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
49 |
| Issue:
|
1 |
| Year:
|
1999 |
| Pages:
|
45-52 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Sufficient conditions are presented for all bounded solutions of the linear system of delay differential equations \[ (-1)^{m+1}\frac{d^my_i(t)}{dt^m} + \sum ^n_{j=1} q_{ij} y_j(t-h_{jj})=0, \quad m \ge 1, \ i=1,2,\ldots ,n, \] to be oscillatory, where $q_{ij} \varepsilon (-\infty ,\infty )$, $h_{jj} \in (0,\infty )$, $i,j = 1,2,\ldots ,n$. Also, we study the oscillatory behavior of all bounded solutions of the linear system of neutral differential equations \[ (-1)^{m+1} \frac{d^m}{dt^m} (y_i(t)+cy_i(t-g)) + \sum ^n_{j=1} q_{ij} y_j (t-h)=0, \] where $c$, $g$ and $h$ are real constants and $i=1,2,\ldots ,n$. (English) |
| MSC:
|
34K11 |
| MSC:
|
34K40 |
| idZBL:
|
Zbl 0955.34051 |
| idMR:
|
MR1676690 |
| . |
| Date available:
|
2009-09-24T10:19:38Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127465 |
| . |
| Reference:
|
[1] K. Gopalsamy: Oscillatory properties of systems of first order linear delay differential inequalities.Pacific J. Math. 128 (1987), 299–305. Zbl 0634.34054, MR 0888519, 10.2140/pjm.1987.128.299 |
| Reference:
|
[2] K. Gopalsamy and G. Ladas: Oscillations of delay differential equations.J. Austral Math. Soc. Ser. B. 32 (1991), 377–381. MR 1097110, 10.1017/S0334270000008493 |
| Reference:
|
[3] I. Györi and G. Ladas: Oscillation Theory of Delay Differential Equations with Applications.Oxford University Press, Oxford, 1991. MR 1168471 |
| Reference:
|
[4] I. T. Kiguradze: On the oscillation of solutions of the equation ${}^mu/t^m+a(t) |u|^n u=0$.Mat. Sb. 65 (1964), 172–187. (Russian) Zbl 0135.14302, MR 0173060 |
| Reference:
|
[5] G. Ladas and I. P. Stavroulakis: On delay differential inequalities of higher order.Canad. Math. Bull. 25 (1982), 348–354. MR 0668953, 10.4153/CMB-1982-049-8 |
| Reference:
|
[6] Ch. G. Philos: On the existence of the nonoscillatory solutions tending to zero at $\infty $ for differential equations with positive delays.Arch. Math. 36 (1981), 168–178. MR 0619435, 10.1007/BF01223686 |
| . |
