| Title:
|
Oscillation theorems for certain even order neutral differential equations (English) |
| Author:
|
Yang, Qi Gui |
| Author:
|
Cheng, Sui-Sun |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
43 |
| Issue:
|
2 |
| Year:
|
2007 |
| Pages:
|
105-122 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This paper is concerned with a class of even order nonlinear differential equations of the form \[ \frac{d}{dt}\Big ( \Big |\left( x(t)+p(t)x(\tau (t))\right) ^{(n-1)}\Big | ^{\alpha -1}(x(t)+p(t)x(\tau (t)))^{(n-1)}\Big ) +F\big ( t,x(g(t))\big ) =0\,, \] where $n$ is even and $t\ge t_{0}$. By using the generalized Riccati transformation and the averaging technique, new oscillation criteria are obtained which are either extensions of or complementary to a number of existing results. Our results are more general and sharper than some previous results even for second order equations. (English) |
| Keyword:
|
neutral differential equation |
| Keyword:
|
oscillation criterion |
| Keyword:
|
Riccati transform |
| Keyword:
|
averaging method |
| MSC:
|
34K11 |
| idZBL:
|
Zbl 1164.34031 |
| idMR:
|
MR2336963 |
| . |
| Date available:
|
2008-06-06T22:50:47Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/108056 |
| . |
| Reference:
|
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| Reference:
|
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