2005-Oujda International Conference on Nonlinear Analysis,
Oujda, Morocco.
Electronic Journal of Differential Equations,
Conference 14 (2006), pp. 155-162.
Title: Note on the nodal line of the p-Laplacian
Authors: Abdel R. El Amrouss (Univ. Mohamed 1er, Oujda, Maroc)
Zakaria El Allali (Univ. Mohamed 1er, Oujda, Maroc)
Najib Tsouli (Univ. Mohamed 1er, Oujda, Maroc)
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.