| Title:
|
On property (B) of higher order delay differential equations (English) |
| Author:
|
Baculíková, Blanka |
| Author:
|
Džurina, Jozef |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
48 |
| Issue:
|
4 |
| Year:
|
2012 |
| Pages:
|
301-309 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we offer criteria for property (B) and additional asymptotic behavior of solutions of the $n$-th order delay differential equations
\begin{equation*} \big (r(t)\big [x^{(n-1)}(t)\big ]^{\gamma }\big )^{\prime }=q(t)f\big (x(\tau (t))\big )\,. \end{equation*}
Obtained results essentially use new comparison theorems, that permit to reduce the problem of the oscillation of the n-th order equation to the the oscillation of a set of certain the first order equations. So that established comparison principles essentially simplify the examination of studied equations. Both cases $\int ^{\infty } r^{-1/\gamma }(t)\,{t}=\infty $ and $\int ^{\infty } r^{-1/\gamma }(t)\,{t}<\infty $ are discussed. (English) |
| Keyword:
|
$n$-th order differential equations |
| Keyword:
|
comparison theorem |
| Keyword:
|
oscillation |
| Keyword:
|
property (B) |
| MSC:
|
34C10 |
| MSC:
|
34K11 |
| idMR:
|
MR3007612 |
| DOI:
|
10.5817/AM2012-4-301 |
| . |
| Date available:
|
2012-12-17T13:54:45Z |
| Last updated:
|
2013-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143104 |
| . |
| Reference:
|
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