Mixed local and nonlocal eigenvalue problems in the exterior domain

IF 2.5 2区数学 Q1 MATHEMATICS

Fractional Calculus and Applied Analysis Pub Date : 2025-05-05 DOI:10.1007/s13540-025-00416-2

R. Lakshmi, Sekhar Ghosh

引用次数: 0

Abstract

This paper aims to study the eigenvalue problems of a mixed local and nonlocal operator in the exterior of a nonempty, bounded, simply connected domain \(\varOmega \subset {\mathbb {R}}^N\) with Lipschitz boundary \(\partial \varOmega \ne \emptyset \). By employing the variational methods combined with the Ljusternik-Schnirelmann principle, we prove the existence of a non-decreasing sequence of eigenvalues. In particular, we prove the principal eigenvalue is simple and isolated. We establish the positivity of the first eigenfunction by obtaining a strong maximum principle. The results obtained here are new even for the case \(p=2\).

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外域的混合局部和非局部特征值问题

研究具有Lipschitz边界\(\partial \varOmega \ne \emptyset \)的非空有界单连通域\(\varOmega \subset {\mathbb {R}}^N\)外的混合局部算子和非局部算子的特征值问题。利用变分方法结合Ljusternik-Schnirelmann原理，证明了特征值非递减序列的存在性。特别地，我们证明了主特征值是简单且孤立的。通过得到一个强极大值原理，建立了第一特征函数的正性。这里得到的结果是新的情况下\(p=2\)。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.