Note on the nodal line of the p-Laplacian

In this paper, we prove that the length of the nodal line of the eigenfunctions associated to the second eigenvalue of the problem $$ -Delta_p u = lambda ho (x) |u|^{p-2}u quad hbox{in } Omega $$ with the Dirichlet conditions is not bounded uniformly with respect to the weight.

Bibliographic Details
Main Authors:	Abdel R. El Amrouss, Zakaria El Allali, Najib Tsouli
Format:	Article
Language:	English
Published:	Texas State University 2006-09-01
Series:	Electronic Journal of Differential Equations
Subjects:	Nonlinear eigenvalue problem p-Laplacian nodal line.
Online Access:	http://ejde.math.txstate.edu/conf-proc/14/e1/abstr.html

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spelling	doaj-04ed5d9af83845f0aab8cd3e2d0c3a782020-11-24T23:10:29ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912006-09-01Conference14155162Note on the nodal line of the p-LaplacianAbdel R. El AmroussZakaria El AllaliNajib TsouliIn this paper, we prove that the length of the nodal line of the eigenfunctions associated to the second eigenvalue of the problem $$ -Delta_p u = lambda ho (x) \|u\|^{p-2}u quad hbox{in } Omega $$ with the Dirichlet conditions is not bounded uniformly with respect to the weight. http://ejde.math.txstate.edu/conf-proc/14/e1/abstr.htmlNonlinear eigenvalue problemp-Laplaciannodal line.
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Abdel R. El Amrouss Zakaria El Allali Najib Tsouli
spellingShingle	Abdel R. El Amrouss Zakaria El Allali Najib Tsouli Note on the nodal line of the p-Laplacian Electronic Journal of Differential Equations Nonlinear eigenvalue problem p-Laplacian nodal line.
author_facet	Abdel R. El Amrouss Zakaria El Allali Najib Tsouli
author_sort	Abdel R. El Amrouss
title	Note on the nodal line of the p-Laplacian
title_short	Note on the nodal line of the p-Laplacian
title_full	Note on the nodal line of the p-Laplacian
title_fullStr	Note on the nodal line of the p-Laplacian
title_full_unstemmed	Note on the nodal line of the p-Laplacian
title_sort	note on the nodal line of the p-laplacian
publisher	Texas State University
series	Electronic Journal of Differential Equations
issn	1072-6691
publishDate	2006-09-01
description	In this paper, we prove that the length of the nodal line of the eigenfunctions associated to the second eigenvalue of the problem $$ -Delta_p u = lambda ho (x) \|u\|^{p-2}u quad hbox{in } Omega $$ with the Dirichlet conditions is not bounded uniformly with respect to the weight.
topic	Nonlinear eigenvalue problem p-Laplacian nodal line.
url	http://ejde.math.txstate.edu/conf-proc/14/e1/abstr.html
work_keys_str_mv	AT abdelrelamrouss noteonthenodallineoftheplaplacian AT zakariaelallali noteonthenodallineoftheplaplacian AT najibtsouli noteonthenodallineoftheplaplacian
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Note on the nodal line of the p-Laplacian

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