| Title:
|
A la recherche du spectre perdu: An invitation to nonlinear spectral theory (English) |
| Author:
|
Appell, Jürgen |
| Language:
|
English |
| Journal:
|
Nonlinear Analysis, Function Spaces and Applications |
| Volume:
|
Vol. 7 |
| Issue:
|
2002 |
| Year:
|
|
| Pages:
|
1-20 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We give a survey on spectra for various classes of nonlinear operators, with a particular emphasis on a comparison of their advantages and drawbacks. Here the most useful spectra are the asymptotic spectrum by M. Furi, M. Martelli and A. Vignoli (1978), the global spectrum by W. Feng (1997), and the local spectrum (called “phantom”) by P. Santucci and M. Väth (2000). In the last part we discuss these spectra for homogeneous operators (of any degree), and derive a discreteness result and a nonlinear Fredholm alternative for such operators. This may be applied to an eigenvalue problem for the $p$-Laplace operator which arises in various fields of applied mathematics, mechanics, and physics. (English) |
| Keyword:
|
Nonlinear spectrum |
| Keyword:
|
nonlinear eigenvalue problem |
| Keyword:
|
homogeneous operator |
| Keyword:
|
coincidence theorem |
| Keyword:
|
discreteness theorem |
| Keyword:
|
nonlinear Fredholm alternative |
| Keyword:
|
$p$-Laplace operator |
| MSC:
|
35J60 |
| MSC:
|
47A10 |
| MSC:
|
47H09 |
| MSC:
|
47H10 |
| MSC:
|
47J05 |
| MSC:
|
47J10 |
| MSC:
|
47J25 |
| . |
| Date available:
|
2009-10-08T09:49:25Z |
| Last updated:
|
2012-08-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/702482 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[3] Appell J., Giorgieri E., Väth M.: Nonlinear spectral theory for homogeneous operators.Nonlinear Funct. Anal. Appl. 7 (2002), 589–618. Zbl 1045.47053, MR 1959638 |
| Reference:
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[4] Binding P. A., Drábek P., Huang Y. X.: On the Fredholm alternative for the $p$-Laplacian.Proc. Amer. Math. Soc. 125 (1997), 3555–3559. Zbl 0882.35049, MR 98b:35058. Zbl 0882.35049, MR 1416077 |
| 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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