| Title:
|
Soliton solutions for quasilinear Schrödinger equation with critical exponential growth in $\mathbb {R}^N$ (English) |
| Author:
|
Chen, Caisheng |
| Author:
|
Song, Hongxue |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
61 |
| Issue:
|
3 |
| Year:
|
2016 |
| Pages:
|
317-337 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this work, we study the existence of nonnegative and nontrivial solutions for the quasilinear Schrödinger equation $$ -\Delta _Nu+b|u|^{N-2}u-\Delta _N(u^2)u=h(u), \quad x\in \mathbb {R}^N, $$ where $\Delta _N$ is the $N$-Laplacian operator, $h(u)$ is continuous and behaves as $\exp (\alpha |u|^{{N}/{(N-1)}})$ when $|u|\to \infty $. Using the Nehari manifold method and the Schwarz symmetrization with some special techniques, the existence of a nonnegative and nontrivial solution $u(x)\in W^{1,N}(\mathbb {R}^N)$ with $u(x)\to 0$ as $|x|\to \infty $ is established. (English) |
| Keyword:
|
$N$-Laplacian equation |
| Keyword:
|
critical exponential growth |
| Keyword:
|
Schwarz symmetrization |
| Keyword:
|
Nehari manifold |
| MSC:
|
35D30 |
| MSC:
|
35J20 |
| MSC:
|
35J92 |
| idZBL:
|
Zbl 06587855 |
| idMR:
|
MR3502114 |
| DOI:
|
10.1007/s10492-016-0134-x |
| . |
| Date available:
|
2016-05-19T08:57:51Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/145704 |
| . |
| Reference:
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