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

Julián Fernández Bonder; Julio D. Rossi

Publicacions Matemàtiques (2002)

  • Volume: 46, Issue: 1, page 221-235
  • ISSN: 0214-1493

Abstract

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In this paper we study the Sobolev trace embedding W1,p(Ω) → LpV (∂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.

How to cite

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Fernández Bonder, Julián, and Rossi, Julio D.. "A nonlinear eigenvalue problem with indefinite weights related to the Sobolev trace embedding.." Publicacions Matemàtiques 46.1 (2002): 221-235. <http://eudml.org/doc/41452>.

@article{FernándezBonder2002,
abstract = {In this paper we study the Sobolev trace embedding W1,p(Ω) → LpV (∂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 = {Fernández Bonder, Julián, Rossi, Julio D.},
journal = {Publicacions Matemàtiques},
keywords = {Ecuaciones diferenciales no lineales; Ecuaciones diferenciales elípticas; Problemas de autovalores; Operador laplaciano; Condiciones de contorno; Inmersiones; -Laplacian; eigenvalue problem; nonlinear boundary conditions; first eigenvalue; second eigenvalue},
language = {eng},
number = {1},
pages = {221-235},
title = {A nonlinear eigenvalue problem with indefinite weights related to the Sobolev trace embedding.},
url = {http://eudml.org/doc/41452},
volume = {46},
year = {2002},
}

TY - JOUR
AU - Fernández Bonder, Julián
AU - Rossi, Julio D.
TI - A nonlinear eigenvalue problem with indefinite weights related to the Sobolev trace embedding.
JO - Publicacions Matemàtiques
PY - 2002
VL - 46
IS - 1
SP - 221
EP - 235
AB - In this paper we study the Sobolev trace embedding W1,p(Ω) → LpV (∂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.
LA - eng
KW - Ecuaciones diferenciales no lineales; Ecuaciones diferenciales elípticas; Problemas de autovalores; Operador laplaciano; Condiciones de contorno; Inmersiones; -Laplacian; eigenvalue problem; nonlinear boundary conditions; first eigenvalue; second eigenvalue
UR - http://eudml.org/doc/41452
ER -

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