| Title:
|
On the oscillation of a class of linear homogeneous third order differential equations (English) |
| Author:
|
Parhi, N. |
| Author:
|
Das, P. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
34 |
| Issue:
|
4 |
| Year:
|
1998 |
| Pages:
|
435-443 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we have considered completely the equation \[ y^{\prime \prime \prime }+ a(t)y^{\prime \prime }+ b(t)y^\prime + c(t)y=0\,, \qquad \mathrm {(*)}\] where $a\in C^2([\sigma , \infty ), R)$, $b\in C^1([\sigma , \infty ),R)$, $c\in C([\sigma , \infty ), R)$ and $\sigma \in R$ such that $a(t)\le 0$, $b(t)\le 0$ and $c(t)\le 0$. It has been shown that the set of all oscillatory solutions of (*) forms a two-dimensional subspace of the solution space of (*) provided that (*) has an oscillatory solution. This answers a question raised by S. Ahmad and A. C. Lazer earlier. (English) |
| Keyword:
|
third order differential equations |
| Keyword:
|
oscillation |
| Keyword:
|
nonoscillation |
| Keyword:
|
asymptotic behaviour of solutions |
| MSC:
|
34C10 |
| MSC:
|
34C11 |
| MSC:
|
34D05 |
| idZBL:
|
Zbl 0973.34023 |
| idMR:
|
MR1679638 |
| . |
| Date available:
|
2009-02-17T10:15:49Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107671 |
| . |
| Reference:
|
[1] Ahmad, S., Lazer, A. C.: On the oscillatory behaviour of a class of linear third order differential equations.J. Math. Anal. Appl. 28(1970), 681-689, MR 40#1646. MR 0248394 |
| Reference:
|
[2] Hanan, M.: Oscillation criteria for a third order linear differential equations.Pacific J. Math. 11(1961), 919-944, MR 26# 2695. MR 0145160 |
| Reference:
|
[3] Jones, G. D.: Properties of solutions of a class of third order differential equations.J. Math. Anal. Appl. 48(1974), 165-169. Zbl 0289.34046, MR 0352608 |
| Reference:
|
[4] Lazer, A. C.: The behaviour of solutions of the differential equation $y^{\prime \prime \prime }+ p(x)y^\prime + q(x)y=0$.Pacific J. Math. 17(1966), 435-466, MR 33#1552. MR 0193332 |
| Reference:
|
[5] Leighton, W., Nehari, Z.: On the oscillation of self adjoint linear differential equations of the fourth order.Trans. Amer. Math. Soc. 89(1958), 325-377. MR 0102639 |
| Reference:
|
[6] Parhi, N., Das, P.: On asymptotic property of solutions of a class of third order differential equations.Proc. Amer. Math. Soc. 110(1990), 387-393. MR 1019279 |
| . |
