In this paper we develop a comprehensive study on principal eigenvalues and both the (weak and strong) maximum and comparison principles related to an important class of nonlinear systems involving fractional m-Laplacian operators. Explicit lower bounds for principal eigenvalues of this system in terms of the diameter of bounded domain \(\varOmega \subset {\mathbb {R}}^N\) are also proved. As application, we measure explicitly how small has to be \(\text {diam}(\varOmega )\) so that weak and strong maximum principles associated to this problem hold in \(\varOmega \).

中文翻译：

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分数 m-拉普拉斯系统的主曲线以及相关的最大值和比较原理

在本文中，我们对涉及分数 m 拉普拉斯算子的一​​类重要的非线性系统相关的主特征值以及（弱和强）最大值和比较原理进行了全面的研究。还证明了该系统的主特征值的显式下界，以有界域 \(\varOmega \subset {\mathbb {R}}^N\) 的直径表示。作为应用，我们明确测量 \(\text {diam}(\varOmega )\) 必须有多小，以便与该问题相关的弱和强最大原理在 \(\varOmega \) 中成立。