| Title:
|
Stationary solutions of semilinear Schrödinger equations with trapping potentials in supercritical dimensions (English) |
| Author:
|
Ficek, Filip |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
59 |
| Issue:
|
1 |
| Year:
|
2023 |
| Pages:
|
31-38 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Nonlinear Schrödinger equations are usually investigated with the use of the variational methods that are limited to energy-subcritical dimensions. Here we present the approach based on the shooting method that can give the proof of existence of the ground states in critical and supercritical cases. We formulate the assumptions on the system that are sufficient for this method to work. As examples, we consider Schrödinger-Newton and Gross-Pitaevskii equations with harmonic potentials. (English) |
| Keyword:
|
nonlinear Schrödinger equation |
| Keyword:
|
stationary solutions |
| Keyword:
|
supercritical dimensions |
| Keyword:
|
shooting method |
| MSC:
|
34B15 |
| MSC:
|
34B18 |
| MSC:
|
35Q55 |
| idZBL:
|
Zbl 07675572 |
| idMR:
|
MR4563014 |
| DOI:
|
10.5817/AM2023-1-31 |
| . |
| Date available:
|
2023-02-22T14:22:21Z |
| Last updated:
|
2023-05-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/151548 |
| . |
| Reference:
|
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| . |
