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Abstract:

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.

Registro:

Documento: Artículo
Título:A nonlinear eigenvalue problem with indefinite weights related to the Sobolev trace embedding
Autor:Fernández Bonder, J.; Rossi, J.D.
Filiación:Departamento de Matemática, FCEyN, Universidad de Buenos Aires, (1428) Buenos Aires, Argentina
Palabras clave:Eigenvalue problems; Nonlinear boundary conditions; p-Laplacian
Año:2002
Volumen:46
Número:1
Página de inicio:221
Página de fin:235
DOI: http://dx.doi.org/10.5565/PUBLMAT_46102_12
Título revista:Publicacions Matematiques
Título revista abreviado:Publ. Mat.
ISSN:02141493
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02141493_v46_n1_p221_FernandezBonder

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Citas:

---------- APA ----------
Fernández Bonder, J. & Rossi, J.D. (2002) . A nonlinear eigenvalue problem with indefinite weights related to the Sobolev trace embedding. Publicacions Matematiques, 46(1), 221-235.
http://dx.doi.org/10.5565/PUBLMAT_46102_12
---------- CHICAGO ----------
Fernández Bonder, J., Rossi, J.D. "A nonlinear eigenvalue problem with indefinite weights related to the Sobolev trace embedding" . Publicacions Matematiques 46, no. 1 (2002) : 221-235.
http://dx.doi.org/10.5565/PUBLMAT_46102_12
---------- MLA ----------
Fernández Bonder, J., Rossi, J.D. "A nonlinear eigenvalue problem with indefinite weights related to the Sobolev trace embedding" . Publicacions Matematiques, vol. 46, no. 1, 2002, pp. 221-235.
http://dx.doi.org/10.5565/PUBLMAT_46102_12
---------- VANCOUVER ----------
Fernández Bonder, J., Rossi, J.D. A nonlinear eigenvalue problem with indefinite weights related to the Sobolev trace embedding. Publ. Mat. 2002;46(1):221-235.
http://dx.doi.org/10.5565/PUBLMAT_46102_12