| Title:
|
Oscillation of unstable second order neutral differential equations with mixed argument (English) |
| Author:
|
Džurina, Jozef |
| Author:
|
Pirč, Viktor |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
130 |
| Issue:
|
3 |
| Year:
|
2005 |
| Pages:
|
323-333 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The aim of this paper is to present new oscillatory criteria for the second order neutral differential equation with mixed argument \[ (x(t)-px(t-\tau ))^{\prime \prime }- q(t)x(\sigma (t))=0. \] The results include also sufficient conditions for bounded and unbounded oscillation of the equations considered. (English) |
| Keyword:
|
neutral equation |
| Keyword:
|
mixed argument |
| MSC:
|
34C10 |
| MSC:
|
34K11 |
| MSC:
|
34K40 |
| idZBL:
|
Zbl 1114.34047 |
| idMR:
|
MR2164661 |
| DOI:
|
10.21136/MB.2005.134096 |
| . |
| Date available:
|
2009-09-24T22:21:43Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134096 |
| . |
| Reference:
|
[1] D. D. Bainov, D. P. Mishev: Oscillation Theory for Neutral Differential Equations with Delay.Adam Hilger, 1991. MR 1147908 |
| Reference:
|
[2] T. A. Chanturia, R. G. Koplatadze: On Oscillatory Properties of Differential Equations with Deviating Arguments.Tbilisi, Univ. Press, Tbilisi, 1977. (Russian) |
| Reference:
|
[3] J. Dzurina, B. Mihalikova: A note on unstable neutral differential equations of the second order.Math. Fascic. 29 (1999), 17–22. MR 1724462 |
| Reference:
|
[4] L. H. Erbe, Q. Kong, B. G. Zhang: Oscillation Theory for Functional Differential Equations.Marcel Dekker, New York, 1995. MR 1309905 |
| Reference:
|
[5] I. Győri, G. Ladas: Theory of Delay Differential Equations with Applications.Clarendon Press, Oxford, 1991. MR 1168471 |
| Reference:
|
[6] G. S. Ladde, V. Lakshmikantham, B. G. Zhang: Oscillation Theory of Differential Equations with Deviating Arguments.Dekker, New York, 1987. MR 1017244 |
| Reference:
|
[7] J. S. Yu, 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, B. G. Zhang: The existence of positive solution and bounded oscillation for second-order neutral differential equations of unstable type.J. Syst. Sci. Math. 16 (1996), 92–96. MR 1404160 |
| 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, 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. Zbl 0754.34075, MR 1159633, 10.1016/0022-247X(92)90322-5 |
| . |
