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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Detalles Bibliográficos
Autores principales:	Fernandez Bonder, Julian, Rossi, Julio Daniel
Publicado:	2002
Materias:	Eigenvalue problems Nonlinear boundary conditions p-Laplacian
Acceso en línea:	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02141493_v46_n1_p221_FernandezBonder 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

id	paper:paper_02141493_v46_n1_p221_FernandezBonder
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spelling	paper:paper_02141493_v46_n1_p221_FernandezBonder2023-06-08T15:20:51Z A nonlinear eigenvalue problem with indefinite weights related to the Sobolev trace embedding Fernandez Bonder, Julian Rossi, Julio Daniel 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. 2002 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02141493_v46_n1_p221_FernandezBonder 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 Fernandez Bonder, Julian Rossi, Julio Daniel 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.
author	Fernandez Bonder, Julian Rossi, Julio Daniel
author_facet	Fernandez Bonder, Julian Rossi, Julio Daniel
author_sort	Fernandez Bonder, Julian
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
publishDate	2002
url	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02141493_v46_n1_p221_FernandezBonder http://hdl.handle.net/20.500.12110/paper_02141493_v46_n1_p221_FernandezBonder
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A nonlinear eigenvalue problem with indefinite weights related to the Sobolev trace embedding

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