2005-Oujda International Conference on Nonlinear Analysis, Oujda, Morocco.
Electron. J. Diff. Eqns., Conference 14 (2006), pp. 155-162.

Note on the nodal line of the p-Laplacian

Abdel R. El Amrouss, Zakaria El Allali, Najib Tsouli

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

Published September 20, 2006.
Math Subject Classifications: 58E05, 35J65, 56J20.
Key Words: Nonlinear eigenvalue problem; p-Laplacian; nodal line.

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Abdelrachid El Amrouss
University Mohamed I, Faculty of sciences
Department of Mathematics, Oujda, Morocco
e-mail: amrouss@sciences.univ-oujda.ac.ma
Zakaria El Allali
University Mohamed I, Faculty of sciences
Department of Mathematics, Oujda, Morocco
e-mail: zakaria@sciences.univ-oujda.ac.ma
Najib Tsouli
University Mohamed I, Faculty of sciences
Department of Mathematics, Oujda, Morocco
e-mail: tsouli@sciences.univ-oujda.ac.ma

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