分数 m-Laplacian 系统的主曲线及相关的最大值和比较原则

IF 2.5 2区数学 Q1 MATHEMATICS

Fractional Calculus and Applied Analysis Pub Date : 2024-05-20 DOI:10.1007/s13540-024-00293-1

Anderson L. A. de Araujo, Edir J. F. Leite, Aldo H. S. Medeiros

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引用次数: 0

摘要

在本文中，我们对涉及分数 m-Laplacian 算子的一类重要非线性系统的主特征值以及（弱和强）最大值和比较原则进行了全面研究。我们还证明了该系统的主特征值在有界域 $\varOmega \subset {\mathbb {R}}^N$ 的直径方面的明确下限。作为应用，我们明确地测量了 $\text {diam}(\varOmega )$ 必须有多小才能使与这个问题相关的弱最大原则和强最大原则在 $\varOmega $ 中成立。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

$Principal curves to fractional m-Laplacian systems and related maximum and comparison principles$

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Principal curves to fractional m-Laplacian systems and related maximum and comparison principles

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 $.

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来源期刊

Fractional Calculus and Applied Analysis MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

4.70

自引率

16.70%

发文量

101

期刊介绍： Fractional Calculus and Applied Analysis (FCAA, abbreviated in the World databases as Fract. Calc. Appl. Anal. or FRACT CALC APPL ANAL) is a specialized international journal for theory and applications of an important branch of Mathematical Analysis (Calculus) where differentiations and integrations can be of arbitrary non-integer order. The high standards of its contents are guaranteed by the prominent members of Editorial Board and the expertise of invited external reviewers, and proven by the recently achieved high values of impact factor (JIF) and impact rang (SJR), launching the journal to top places of the ranking lists of Thomson Reuters and Scopus.