A nonlinear eigenvalue problem with indefinite weights related to the Sobolev trace embedding

In this paper we study the Sobolev trace embedding W1,p(Ω) rightwards arrow with hook LV p(∂Ω), where V is an indefinite weight. This embedding leads to a nonlinear eigenvalue problem where the eigenvalue appears at the (nonlinear) boundary condition. We prove that there exists a sequence of variati...

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Autores principales: Fernández Bonder, J., Rossi, J.D.
Formato: JOUR
Materias:
Eigenvalue problems
Nonlinear boundary conditions
p-Laplacian
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_02141493_v46_n1_p221_FernandezBonder
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling todo:paper_02141493_v46_n1_p221_FernandezBonder2023-10-03T15:10:11Z A nonlinear eigenvalue problem with indefinite weights related to the Sobolev trace embedding Fernández Bonder, J. Rossi, J.D. Eigenvalue problems Nonlinear boundary conditions p-Laplacian In this paper we study the Sobolev trace embedding W1,p(Ω) rightwards arrow with hook LV p(∂Ω), where V is an indefinite weight. This embedding leads to a nonlinear eigenvalue problem where the eigenvalue appears at the (nonlinear) boundary condition. We prove that there exists a sequence of variational eigenvalues λk ↗ +∞ and then show that the first eigenvalue is isolated, simple and monotone with respect to the weight. Then we prove a nonexistence result related to the first eigenvalue and we end this article with the study of the second eigenvalue proving that it coincides with the second variational eigenvalue. Fil:Fernández Bonder, J. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Rossi, J.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_02141493_v46_n1_p221_FernandezBonder
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Eigenvalue problems
Nonlinear boundary conditions
p-Laplacian
spellingShingle Eigenvalue problems
Nonlinear boundary conditions
p-Laplacian
Fernández Bonder, J.
Rossi, J.D.
A nonlinear eigenvalue problem with indefinite weights related to the Sobolev trace embedding
topic_facet Eigenvalue problems
Nonlinear boundary conditions
p-Laplacian
description In this paper we study the Sobolev trace embedding W1,p(Ω) rightwards arrow with hook LV p(∂Ω), where V is an indefinite weight. This embedding leads to a nonlinear eigenvalue problem where the eigenvalue appears at the (nonlinear) boundary condition. We prove that there exists a sequence of variational eigenvalues λk ↗ +∞ and then show that the first eigenvalue is isolated, simple and monotone with respect to the weight. Then we prove a nonexistence result related to the first eigenvalue and we end this article with the study of the second eigenvalue proving that it coincides with the second variational eigenvalue.
format JOUR
author Fernández Bonder, J.
Rossi, J.D.
author_facet Fernández Bonder, J.
Rossi, J.D.
author_sort Fernández Bonder, J.
title A nonlinear eigenvalue problem with indefinite weights related to the Sobolev trace embedding
title_short A nonlinear eigenvalue problem with indefinite weights related to the Sobolev trace embedding
title_full A nonlinear eigenvalue problem with indefinite weights related to the Sobolev trace embedding
title_fullStr A nonlinear eigenvalue problem with indefinite weights related to the Sobolev trace embedding
title_full_unstemmed A nonlinear eigenvalue problem with indefinite weights related to the Sobolev trace embedding
title_sort nonlinear eigenvalue problem with indefinite weights related to the sobolev trace embedding
url http://hdl.handle.net/20.500.12110/paper_02141493_v46_n1_p221_FernandezBonder
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AT fernandezbonderj nonlineareigenvalueproblemwithindefiniteweightsrelatedtothesobolevtraceembedding
AT rossijd nonlineareigenvalueproblemwithindefiniteweightsrelatedtothesobolevtraceembedding
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