Note on the nodal line of the p-Laplacian

Abstract

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

Keywords

• Nonlinear eigenvalue problem
• p-Laplacian
• nodal line.