Full description of the eigenvalue set of the $(p,q)$-Laplacian with a Steklov-like boundary condition

Abstract

In this paper we consider in a bounded domain $\Omega \subset {\mathbb{R}}^N$ with smooth boundary an eigenvalue problem for the negative $(p,q)$-Laplacian with a Steklov-like boundary condition, where $p,q\in (1,\infty )$, $p\ne q$, including the open case $p\in (1,\infty )$, $q\in (1,2)$, $p\ne q$. A full description of the set of eigenvalues of this problem is provided. Our results complement those previously obtained by Abreu and Madeira \cite{AM}, Barbu and Moroşanu \cite{BM}, Fărcăşeanu, Mihăilescu and Stancu-Dumitru \cite{FMS}, Mihăilescu \cite{MMih}, Mihăilescu and Moroşanu \cite{MM}.

arXiv admin note: text overlap with arXiv:1703.04050