| Title:
|
Oscillation of a higher order neutral differential equation with a sub-linear delay term and positive and negative coefficients (English) |
| Author:
|
Dix, Julio G. |
| Author:
|
Ghose, Dillip Kumar |
| Author:
|
Rath, Radhanath |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
134 |
| Issue:
|
4 |
| Year:
|
2009 |
| Pages:
|
411-425 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We obtain sufficient conditions for every solution of the differential equation $$ [y(t)-p(t)y(r(t))]^{(n)}+v(t)G(y(g(t)))-u(t)H(y(h(t)))=f(t) $$ to oscillate or to tend to zero as $t$ approaches infinity. In particular, we extend the results of Karpuz, Rath and Padhy (2008) to the case when $G$ has sub-linear growth at infinity. Our results also apply to the neutral equation $$ [y(t)-p(t)y(r(t))]^{(n)}+q(t)G(y(g(t)))=f(t) $$ when $q(t)$ has sign changes. Both bounded and unbounded solutions are consideted here; thus some known results are expanded. (English) |
| Keyword:
|
oscillatory solution |
| Keyword:
|
neutral differential equation |
| Keyword:
|
asymptotic behaviour |
| MSC:
|
34C10 |
| MSC:
|
34C15 |
| MSC:
|
34K40 |
| idZBL:
|
Zbl 1212.34191 |
| idMR:
|
MR2597236 |
| DOI:
|
10.21136/MB.2009.140673 |
| . |
| Date available:
|
2010-07-20T18:14:13Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140673 |
| . |
| Reference:
|
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