A pathological example in nonlinear spectral theory

Abstract

We construct an open set Ω⊂ℝN{\Omega\subset\mathbb{R}^{N}} on which an eigenvalue problem for the p-Laplacian has no isolated first eigenvalue and the spectrum is not discrete. The same example shows that the usual Lusternik–Schnirelmann minimax construction does not exhaust the whole spectrum of this eigenvalue problem.

Keywords

• nonlinear eigenvalue problems
• lusternik–schnirelmann theory
• 35p30
• 47a75
• 58e05