*Accepted Paper*

**Inserted:** 24 feb 2017

**Last Updated:** 4 jul 2017

**Journal:** Adv. Nonlinear Anal.

**Pages:** 9

**Year:** 2017

**Notes:**

We construct an open set $\Omega\subset\mathbb{R}^N$ on which an eigenvalue problem for the $p-$Laplacian has not 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:**
p-Laplacian, Nonlinear eigenvalue problems, Lusternik-Schnirelmann theory

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