| Title:
|
Solutions to a perturbed critical semilinear equation concerning the $N$-Laplacian in $\Bbb R^{N}$ (English) |
| Author:
|
Tonkes, Elliot |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
40 |
| Issue:
|
4 |
| Year:
|
1999 |
| Pages:
|
679-699 |
| . |
| Category:
|
math |
| . |
| Summary:
|
The aim of this paper is to study the existence of variational solutions to a nonhomogeneous elliptic equation involving the $N$-Laplacian $$ - \Delta_N u \equiv - \operatorname{div} (|\nabla u|^{N-2} \nabla u) = e(x,u) + h(x) \text{ in } \Omega $$ where $u \in W_0^{1,N}(\Bbb R^{N})$, $\Omega$ is a bounded smooth domain in $\Bbb R^{N}$, $N \geq 2$, $e(x,u)$ is a critical nonlinearity in the sense of the Trudinger-Moser inequality and $h(x) \in (W_0^{1,N})^*$ is a small perturbation. (English) |
| Keyword:
|
variational methods |
| Keyword:
|
elliptic equations |
| Keyword:
|
critical growth |
| MSC:
|
35B20 |
| MSC:
|
35B33 |
| MSC:
|
35B34 |
| MSC:
|
35J20 |
| MSC:
|
35J60 |
| MSC:
|
35J65 |
| idZBL:
|
Zbl 1064.35511 |
| idMR:
|
MR1756545 |
| . |
| Date available:
|
2009-01-08T18:56:36Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119123 |
| . |
| Reference:
|
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| Reference:
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| . |
