| Title:
|
On unstable neutral differential equations of the second order (English) |
| Author:
|
Džurina, Jozef |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
52 |
| Issue:
|
4 |
| Year:
|
2002 |
| Pages:
|
739-747 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The aim of this paper is to present sufficient conditions for all bounded solutions of the second order neutral differential equation \[ \big (x(t)-px(t-\tau )\big )^{\prime \prime }- q(t)x\big (\sigma (t)\big )=0 \] to be oscillatory and to improve some existing results. The main results are based on the comparison principles. (English) |
| Keyword:
|
neutral equation |
| Keyword:
|
delayed argument |
| MSC:
|
34C10 |
| MSC:
|
34K11 |
| MSC:
|
34K20 |
| MSC:
|
34K40 |
| idZBL:
|
Zbl 1023.34057 |
| idMR:
|
MR1940055 |
| . |
| Date available:
|
2009-09-24T10:56:13Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127760 |
| . |
| Reference:
|
[1] D. D. Bainov and D. P. Mishev: Oscillation Theory for Neutral Differential Equations with Delay.Adam Hilger, Bristol, 1991. MR 1147908 |
| Reference:
|
[2] T. A. Čanturia and R. G. Koplatadze: On oscillatory properties of differential equations with deviating arguments.Tbilisi, Univ. Press, Tbilisi, 1977. (Russian) |
| Reference:
|
[3] L. H. Erbe, Q. Kong and B. G. Zhang: Oscillation Theory for Functional Differential Equations.Dekker, New York, 1995. MR 1309905 |
| Reference:
|
[4] I. Győri and G. Ladas: Theory of Delay Differential Equations with Applications.Clarendon Press, Oxford, 1991. MR 1168471 |
| Reference:
|
[5] J. Jaros and T. Kusano: Sufficient conditions for oscillations in higher order linear functional differential equations of neutral type.Japan. J. Math. 15 (1989), 415–432. MR 1039249, 10.4099/math1924.15.415 |
| Reference:
|
[6] G. S. Ladde, V. Lakshmikantham and B. G. Zhang: Oscillation theory of differential equations with deviating arguments.Dekker, New York, 1987. MR 1017244 |
| Reference:
|
[7] J. S. Yu and Z. C. Wang: Some further result on oscillation of neutral differential equations.Bull. Austral. Math. Soc. 46 (1992), 149–157. MR 1170449, 10.1017/S0004972700011758 |
| Reference:
|
[8] J. S. Yu and B. G. Zhang: The existence of positive solution for second order neutral differential equations with unstable type.Systems Sci. Math. Sci (to appear). |
| Reference:
|
[9] B.G. Zhang: Oscillation of second order neutral differential equations.Kexue Tongbao 34 (1989), 563–566. Zbl 0661.34074, MR 1020422 |
| Reference:
|
[10] B.G. Zhang and J.S. Yu: On the existence of asymptotically decaying positive solutions of second order neutral differential equations.J. Math. Anal. Appl. 166 (1992), 1–11. MR 1159633, 10.1016/0022-247X(92)90322-5 |
| . |
