具有迪里夏特条件的分数 p-拉普拉奇的最优可解性

IF 2.9 2区数学 Q1 MATHEMATICS Fractional Calculus and Applied Analysis Pub Date : 2024-09-13 DOI:10.1007/s13540-024-00341-w

Antonio Iannizzotto, Dimitri Mugnai

{"title":"具有迪里夏特条件的分数 p-拉普拉奇的最优可解性","authors":"Antonio Iannizzotto, Dimitri Mugnai","doi":"10.1007/s13540-024-00341-w","DOIUrl":null,"url":null,"abstract":"We study a nonlinear, nonlocal Dirichlet problem driven by the fractional p-Laplacian, involving a \\((p-1)\\)-sublinear reaction. By means of a weak comparison principle we prove uniqueness of the solution. Also, comparing the problem to ’asymptotic’ weighted eigenvalue problems for the same operator, we prove a necessary and sufficient condition for the existence of a solution. Our work extends classical results due to Brezis-Oswald [7] and Diaz-Saa [11] to the nonlinear nonlocal framework.","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"53 1","pages":""},"PeriodicalIF":2.9000,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Optimal solvability for the fractional p-Laplacian with Dirichlet conditions\",\"authors\":\"Antonio Iannizzotto, Dimitri Mugnai\",\"doi\":\"10.1007/s13540-024-00341-w\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study a nonlinear, nonlocal Dirichlet problem driven by the fractional p-Laplacian, involving a \\\\((p-1)\\\\)-sublinear reaction. By means of a weak comparison principle we prove uniqueness of the solution. Also, comparing the problem to ’asymptotic’ weighted eigenvalue problems for the same operator, we prove a necessary and sufficient condition for the existence of a solution. Our work extends classical results due to Brezis-Oswald [7] and Diaz-Saa [11] to the nonlinear nonlocal framework.\",\"PeriodicalId\":48928,\"journal\":{\"name\":\"Fractional Calculus and Applied Analysis\",\"volume\":\"53 1\",\"pages\":\"\"},\"PeriodicalIF\":2.9000,\"publicationDate\":\"2024-09-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Fractional Calculus and Applied Analysis\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s13540-024-00341-w\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Fractional Calculus and Applied Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s13540-024-00341-w","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

我们研究了一个由分数 p-Laplacian 驱动的非线性、非局部 Dirichlet 问题，其中涉及一个（(p-1)\）次线性反应。通过弱比较原理，我们证明了解的唯一性。同时，通过将该问题与同一算子的 "渐近 "加权特征值问题进行比较，我们证明了解存在的必要条件和充分条件。我们的研究将 Brezis-Oswald [7] 和 Diaz-Saa [11] 的经典结果扩展到了非线性非局部框架。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Optimal solvability for the fractional p-Laplacian with Dirichlet conditions

We study a nonlinear, nonlocal Dirichlet problem driven by the fractional p-Laplacian, involving a \((p-1)\)-sublinear reaction. By means of a weak comparison principle we prove uniqueness of the solution. Also, comparing the problem to ’asymptotic’ weighted eigenvalue problems for the same operator, we prove a necessary and sufficient condition for the existence of a solution. Our work extends classical results due to Brezis-Oswald [7] and Diaz-Saa [11] to the nonlinear nonlocal framework.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

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.