| Title:
|
Eigenvalues of the $p$-Laplacian in ${\boldkey R}^N$ with indefinite weight (English) |
| Author:
|
Huang, Yin Xi |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
36 |
| Issue:
|
3 |
| Year:
|
1995 |
| Pages:
|
519-527 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We consider the nonlinear eigenvalue problem $$ -\operatorname{div}(|{\nabla} u|^{p-2}{\nabla} u)=\lambda g(x)|u|^{p-2}u $$ in $\boldkey R^N$ with $p>1$. A condition on indefinite weight function $g$ is given so that the problem has a sequence of eigenvalues tending to infinity with decaying eigenfunctions in ${W^{1, p}(\boldkey R^N)}$. A nonexistence result is also given for the case $p\geq N$. (English) |
| Keyword:
|
eigenvalue |
| Keyword:
|
the $p$-Laplacian |
| Keyword:
|
indefinite weight |
| Keyword:
|
$\boldkey R^N$ |
| MSC:
|
35J65 |
| MSC:
|
35J70 |
| MSC:
|
35P30 |
| MSC:
|
58E05 |
| idZBL:
|
Zbl 0839.35097 |
| idMR:
|
MR1364493 |
| . |
| Date available:
|
2009-01-08T18:19:52Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118781 |
| . |
| Reference:
|
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| Reference:
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| . |
