| Title:
|
Asymptotic forms of solutions of perturbed half-linear ordinary differential equations (English) |
| Author:
|
Luey, Sokea |
| Author:
|
Usami, Hiroyuki |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
57 |
| Issue:
|
1 |
| Year:
|
2021 |
| Pages:
|
27-39 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Asymptotic forms of solutions of half-linear ordinary differential equation $\big (|u^{\prime }|^{\alpha -1}u^{\prime }\big )^{\prime }= \alpha \big (1+b(t)\big ) |u|^{\alpha -1}u$ are investigated under a smallness condition and some signum conditions on $b(t)$. When $\alpha =1$, our results reduce to well-known ones for linear ordinary differential equations. (English) |
| Keyword:
|
half-linear ordinary differential equation |
| Keyword:
|
asymptotic form |
| MSC:
|
34A34 |
| MSC:
|
34D05 |
| MSC:
|
34E10 |
| idZBL:
|
Zbl 07332702 |
| idMR:
|
MR4260838 |
| DOI:
|
10.5817/AM2021-1-27 |
| . |
| Date available:
|
2021-03-05T10:32:24Z |
| Last updated:
|
2021-11-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148716 |
| . |
| Reference:
|
[1] Bodine, S., Lutz, D.A.: Asymptotic Integration of Differential and Difference Equations.Lecture Notes in Math., vol. 2129, Springer, 2015. MR 3362540 |
| Reference:
|
[2] Coppel, W.A.: Stability and Asymptotic Behavior of Differential Equations.Heath, 1965. Zbl 0154.09301, MR 0190463 |
| Reference:
|
[3] Došlý, O., Řehák, P.: Half-linear Differential Equations.Elsevier, 2005. MR 2158903 |
| Reference:
|
[4] Hartman, P.: Ordinary Differential Equations.Birkhäuser, 1982. Zbl 0476.34002, MR 0658490 |
| Reference:
|
[5] Mizukami, M., Naito, M., Usami, H.: Asymptotic behavior of solutions of a class of second order quasilinear ordinary differential equations.Hiroshima Math. J. 32 (2002), 51–78. Zbl 1017.34053, MR 1892669, 10.32917/hmj/1151007642 |
| Reference:
|
[6] Naito, Y., Tanaka, S.: Sharp conditions for the existence of sign-changing solutions to equations involving the one-dimensional p-Laplacian.Nonlinear Anal. 69 (2008), 3070–3083. MR 2452116 |
| . |
