Eigenvalues of the negative $(p,q)$-Laplacian under a Steklov-like boundary condition

TL;DR

This paper investigates the eigenvalues of a negative $(p,q)$-Laplacian with Steklov boundary conditions in a smooth bounded domain, extending previous results for the $(p,2)$-Laplacian to more general cases.

Contribution

It provides a complete characterization of the eigenvalues for the negative $(p,q)$-Laplacian with Steklov boundary conditions, generalizing recent findings.

Findings

Full description of the eigenvalue set for the problem.

Extension of previous results from the $(p,2)$-Laplacian to the $(p,q)$-Laplacian.

Theoretical framework for eigenvalues under Steklov-like boundary conditions.

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 type boundary condition, where $p\in (1,\infty)$, $q\in (2,\infty)$ and $p\neq q$. A full description of the set of eigenvalues of this problem is provided, thus essentially extending a recent result by Abreu and Madeira [1] related to the $(p,2)$-Laplacian.