| Title:
|
Oscillation of third order differential equation with damping term (English) |
| Author:
|
Bartušek, Miroslav |
| Author:
|
Došlá, Zuzana |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
65 |
| Issue:
|
2 |
| Year:
|
2015 |
| Pages:
|
301-316 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We study asymptotic and oscillatory properties of solutions to the third order differential equation with a damping term $$ x'''(t)+q(t)x'(t)+r(t)|x|^{\lambda }(t)\mathop {\rm sgn} x(t)=0 ,\quad t\geq 0. $$ We give conditions under which every solution of the equation above is either oscillatory or tends to zero. In case $\lambda \leq 1$ and if the corresponding second order differential equation $h''+q(t)h=0$ is oscillatory, we also study Kneser solutions vanishing at infinity and the existence of oscillatory solutions. (English) |
| Keyword:
|
third order nonlinear differential equation |
| Keyword:
|
vanishing at infinity solution |
| Keyword:
|
Kneser solution |
| Keyword:
|
oscillatory solution |
| MSC:
|
34C10 |
| MSC:
|
34C15 |
| idZBL:
|
Zbl 06486947 |
| idMR:
|
MR3360427 |
| DOI:
|
10.1007/s10587-015-0176-3 |
| . |
| Date available:
|
2015-06-16T17:31:56Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144270 |
| . |
| Reference:
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