Existence of multiple principal eigenvalues for some indefinite linear eigenvalue problems

J. Fleckinger; J. Hernández; F. Thélin

Bollettino dell'Unione Matematica Italiana (2004)

  • Volume: 7-B, Issue: 1, page 159-188
  • ISSN: 0392-4041

Abstract

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We study the existence of principal eigenvalues for differential operators of second order which are not necessarily in divergence form. We obtain results concerning multiplicity of principal eigenvalues in both the variational and the general case. Our approach uses systematically the Krein-Rutman theorem and fixed point arguments for the spectral radius of some associated problems. We also use a variational characterization for both the self-adjoint and the general case.

How to cite

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Fleckinger, J., Hernández, J., and Thélin, F.. "Existence of multiple principal eigenvalues for some indefinite linear eigenvalue problems." Bollettino dell'Unione Matematica Italiana 7-B.1 (2004): 159-188. <http://eudml.org/doc/195615>.

@article{Fleckinger2004,
abstract = {We study the existence of principal eigenvalues for differential operators of second order which are not necessarily in divergence form. We obtain results concerning multiplicity of principal eigenvalues in both the variational and the general case. Our approach uses systematically the Krein-Rutman theorem and fixed point arguments for the spectral radius of some associated problems. We also use a variational characterization for both the self-adjoint and the general case.},
author = {Fleckinger, J., Hernández, J., Thélin, F.},
journal = {Bollettino dell'Unione Matematica Italiana},
keywords = {second order differential operator; eigenvalue; eigenfunction; principal eigenvalue; Krein-Rutman theorem; fixed point theorem; spectral radius},
language = {eng},
month = {2},
number = {1},
pages = {159-188},
publisher = {Unione Matematica Italiana},
title = {Existence of multiple principal eigenvalues for some indefinite linear eigenvalue problems},
url = {http://eudml.org/doc/195615},
volume = {7-B},
year = {2004},
}

TY - JOUR
AU - Fleckinger, J.
AU - Hernández, J.
AU - Thélin, F.
TI - Existence of multiple principal eigenvalues for some indefinite linear eigenvalue problems
JO - Bollettino dell'Unione Matematica Italiana
DA - 2004/2//
PB - Unione Matematica Italiana
VL - 7-B
IS - 1
SP - 159
EP - 188
AB - We study the existence of principal eigenvalues for differential operators of second order which are not necessarily in divergence form. We obtain results concerning multiplicity of principal eigenvalues in both the variational and the general case. Our approach uses systematically the Krein-Rutman theorem and fixed point arguments for the spectral radius of some associated problems. We also use a variational characterization for both the self-adjoint and the general case.
LA - eng
KW - second order differential operator; eigenvalue; eigenfunction; principal eigenvalue; Krein-Rutman theorem; fixed point theorem; spectral radius
UR - http://eudml.org/doc/195615
ER -

References

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