A la recherche du spectre perdu: An invitation to nonlinear spectral theory

Appell, Jürgen

  • Nonlinear Analysis, Function Spaces and Applications, Publisher: Czech Academy of Sciences, Mathematical Institute(Praha), page 1-20

Abstract

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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.

How to cite

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Appell, Jürgen. "A la recherche du spectre perdu: An invitation to nonlinear spectral theory." Nonlinear Analysis, Function Spaces and Applications. Praha: Czech Academy of Sciences, Mathematical Institute, 2003. 1-20. <http://eudml.org/doc/221387>.

@inProceedings{Appell2003,
abstract = {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.},
author = {Appell, Jürgen},
booktitle = {Nonlinear Analysis, Function Spaces and Applications},
keywords = {Nonlinear spectrum; nonlinear eigenvalue problem; homogeneous operator; coincidence theorem; discreteness theorem; nonlinear Fredholm alternative; $p$-Laplace operator},
location = {Praha},
pages = {1-20},
publisher = {Czech Academy of Sciences, Mathematical Institute},
title = {A la recherche du spectre perdu: An invitation to nonlinear spectral theory},
url = {http://eudml.org/doc/221387},
year = {2003},
}

TY - CLSWK
AU - Appell, Jürgen
TI - A la recherche du spectre perdu: An invitation to nonlinear spectral theory
T2 - Nonlinear Analysis, Function Spaces and Applications
PY - 2003
CY - Praha
PB - Czech Academy of Sciences, Mathematical Institute
SP - 1
EP - 20
AB - 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.
KW - Nonlinear spectrum; nonlinear eigenvalue problem; homogeneous operator; coincidence theorem; discreteness theorem; nonlinear Fredholm alternative; $p$-Laplace operator
UR - http://eudml.org/doc/221387
ER -

References

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