| Title:
|
The least eigenvalues of nonhomogeneous degenerated quasilinear eigenvalue problems (English) |
| Author:
|
Drábek, Pavel |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
120 |
| Issue:
|
2 |
| Year:
|
1995 |
| Pages:
|
169-195 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove the existence of the least positive eigenvalue with a corresponding nonnegative eigenfunction of the quasilinear eigenvalue problem
\align-\operatorname{div}(a(x,u)|\nablau|^{p-2}\nabla u) = &\lambda b(x,u)|u|^{p-2}u \quad\text{ in } \Omega,
u = &0 \hskip2cm\text{ on } \partial\Omega, \endalign where $\Omega$ is a bounded domain, $p>1$ is a real number and $a(x,u)$, $b(x,u)$ satisfy appropriate growth conditions. Moreover, the coefficient $a(x,u)$ contains a degeneration or a singularity. We work in a suitable weighted Sobolev space and prove the boundedness of the eigenfunction in $L^\infty(\Omega)$. The main tool is the investigation of the associated homogeneous eigenvalue problem and an application of the Schauder fixed point theorem. (English) |
| Keyword:
|
boundedness of eigenfunction |
| Keyword:
|
weighted Sobolev space |
| Keyword:
|
Schauder fixed point theorem |
| Keyword:
|
degenerated quasilinear partial differential equations |
| Keyword:
|
weak solutions |
| Keyword:
|
eigenvalue problems |
| Keyword:
|
boundedness of the solution |
| MSC:
|
35B35 |
| MSC:
|
35B45 |
| MSC:
|
35J20 |
| MSC:
|
35J65 |
| MSC:
|
35J70 |
| MSC:
|
35P30 |
| MSC:
|
47H12 |
| MSC:
|
47N20 |
| idZBL:
|
Zbl 0839.35049 |
| idMR:
|
MR1357600 |
| DOI:
|
10.21136/MB.1995.126227 |
| . |
| Date available:
|
2009-09-24T21:10:09Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126227 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| . |
