| Title:
|
On the inhomogeneous nonlinear Schrödinger equation with harmonic potential and unbounded coefficient (English) |
| Author:
|
Chen, Jianqing |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
60 |
| Issue:
|
3 |
| Year:
|
2010 |
| Pages:
|
715-736 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
By deriving a variant of interpolation inequality, we obtain a sharp criterion for global existence and blow-up of solutions to the inhomogeneous nonlinear Schrödinger equation with harmonic potential $$ {\rm i}\varphi _t=-\triangle \varphi +|x|^2\varphi -|x|^b|\varphi |^{p-2}\varphi . $$ We also prove the existence of unstable standing-wave solutions via blow-up under certain conditions on the unbounded inhomogeneity and the power of nonlinearity, as well as the frequency of the wave. (English) |
| Keyword:
|
interpolation inequality |
| Keyword:
|
inhomogeneous nonlinear Schrödinger equation |
| Keyword:
|
harmonic potential |
| Keyword:
|
blow-up |
| Keyword:
|
global existence |
| Keyword:
|
standing waves |
| Keyword:
|
strong instability |
| MSC:
|
35J20 |
| MSC:
|
35Q55 |
| idZBL:
|
Zbl 1224.35083 |
| idMR:
|
MR2672412 |
| . |
| Date available:
|
2010-07-20T17:14:55Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140601 |
| . |
| Reference:
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