In this paper we consider in a bounded domain $\mathrm{\Omega }\subset {\mathbb{R}}^N$ 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-Madeira [1], Barbu-Moroşanu [2], Fărcăşeanu-Mihăilescu-Stancu Dumitru [9], Mihăilescu [16], Mihăilescu-Moroşanu [17].

中文翻译：

---

Steklov（p，q）-Laplacian特征值集的完整描述

在本文中，我们考虑有界域 $\mathrm{\Omega }\subset {\mathbb{[R}}^{ñ}$ 具有光滑边界的负值特征值问题 $（p，q）$-Laplacian具有类似Steklov的边界条件，其中 $p，q\in （\mathrm{1个}，\infty ）$， $p\ne q$，包括打开的盒子 $p\in （\mathrm{1个}，\infty ）$， $q\in （\mathrm{1个}，\mathrm{2个}）$， $p\ne q$。提供了此问题的特征值集的完整描述。我们的结果补充了先前由Abreu-Madeira [1]，Barbu-Moroşanu[2]，Fărcăşeanu-Mihăilescu-StancuDumitru [9]，Mihăilescu[16]，Mihăilescu-Moroşanu[17]获得的结果。