不定权的非局部特征值问题

IF 0.2 Q4 MATHEMATICS

Methods of Functional Analysis and Topology Pub Date : 2020-09-28 DOI:10.31392/mfat-npu26_3.2020.09

S. Taarabti

{"title":"不定权的非局部特征值问题","authors":"S. Taarabti","doi":"10.31392/mfat-npu26_3.2020.09","DOIUrl":null,"url":null,"abstract":"In the present paper, we consider a class of eigenvalue problems driven by a nonlocal integro-di erential operator \\scrL K with Dirichlet boundary conditions. Under certain assumptions on p and q, we establish that any \\lambda > 0 su ciently small is an eigenvalue of the nonhomogeneous nonlocal problem (\\scrP \\lambda ). ®§£«ï¤ õâìáï a« á á ̄¥aâà «ì ̈å § ¤ ç, ̄®¢'ï§ ̈å ÷§ ¥«®a «ì ̈¬ ÷â¥£à®¤ ̈ä¥à¥æ÷ «ì ̈¬ ® ̄¥à â®à®¬ \\scrL K ÷§ aà ©®¢®î ã¬®¢®î ̈à ̈å«¥. ̄¥¢ ̈å ̄à ̈ ̄ãé¥ì é®¤® p ÷ q ¤®¢¥¤¥®, é® a®¦¥ ¤®áâ ì® ¬ «¥ \\lambda > 0 õ ¢« á ̈¬ § ç¥ï¬ ¥®¤®à÷¤®ù ¥«®a «ì®ù § ¤ ç÷ (\\scrP \\lambda ).","PeriodicalId":44325,"journal":{"name":"Methods of Functional Analysis and Topology","volume":"26 1","pages":"283-294"},"PeriodicalIF":0.2000,"publicationDate":"2020-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Nonlocal eigenvalue problems with indefinite weight\",\"authors\":\"S. Taarabti\",\"doi\":\"10.31392/mfat-npu26_3.2020.09\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In the present paper, we consider a class of eigenvalue problems driven by a nonlocal integro-di erential operator \\\\scrL K with Dirichlet boundary conditions. Under certain assumptions on p and q, we establish that any \\\\lambda > 0 su ciently small is an eigenvalue of the nonhomogeneous nonlocal problem (\\\\scrP \\\\lambda ). ®§£«ï¤ õâìáï a« á á ̄¥aâà «ì ̈å § ¤ ç, ̄®¢'ï§ ̈å ÷§ ¥«®a «ì ̈¬ ÷â¥£à®¤ ̈ä¥à¥æ÷ «ì ̈¬ ® ̄¥à â®à®¬ \\\\scrL K ÷§ aà ©®¢®î ã¬®¢®î ̈à ̈å«¥. ̄¥¢ ̈å ̄à ̈ ̄ãé¥ì é®¤® p ÷ q ¤®¢¥¤¥®, é® a®¦¥ ¤®áâ ì® ¬ «¥ \\\\lambda > 0 õ ¢« á ̈¬ § ç¥ï¬ ¥®¤®à÷¤®ù ¥«®a «ì®ù § ¤ ç÷ (\\\\scrP \\\\lambda ).\",\"PeriodicalId\":44325,\"journal\":{\"name\":\"Methods of Functional Analysis and Topology\",\"volume\":\"26 1\",\"pages\":\"283-294\"},\"PeriodicalIF\":0.2000,\"publicationDate\":\"2020-09-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Methods of Functional Analysis and Topology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.31392/mfat-npu26_3.2020.09\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Methods of Functional Analysis and Topology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.31392/mfat-npu26_3.2020.09","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 2

摘要

在本文中，我们考虑了一类由具有Dirichlet边界条件的非局部积分微分算子\scrL K驱动的特征值问题。在对p和q的某些假设下，我们证明了任何λ>0足够小都是非齐次非局部问题（\scrP\lambda）的特征值。÷®§§§§®“'ï§776；å§”®a 776欧元®® •®属于®ŞscrL K§aà©®“®î®“®编号776à编号776å135-776åà776éé®“® p÷q¢®¢￥®, y® 一®“®白天® λ>0õá776；»®我不知道。®÷®[未知]®对®§§ç÷（\scrP\lambda）。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Nonlocal eigenvalue problems with indefinite weight

In the present paper, we consider a class of eigenvalue problems driven by a nonlocal integro-di erential operator \scrL K with Dirichlet boundary conditions. Under certain assumptions on p and q, we establish that any \lambda > 0 su ciently small is an eigenvalue of the nonhomogeneous nonlocal problem (\scrP \lambda ). ®§£«ï¤ õâìáï a« á á ̄¥aâà «ì ̈å § ¤ ç, ̄®¢'ï§ ̈å ÷§ ¥«®a «ì ̈¬ ÷â¥£à®¤ ̈ä¥à¥æ÷ «ì ̈¬ ® ̄¥à â®à®¬ \scrL K ÷§ aà ©®¢®î ã¬®¢®î ̈à ̈å«¥. ̄¥¢ ̈å ̄à ̈ ̄ãé¥ì é®¤® p ÷ q ¤®¢¥¤¥®, é® a®¦¥ ¤®áâ ì® ¬ «¥ \lambda > 0 õ ¢« á ̈¬ § ç¥ï¬ ¥®¤®à÷¤®ù ¥«®a «ì®ù § ¤ ç÷ (\scrP \lambda ).

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

Methods of Functional Analysis and Topology MATHEMATICS-

CiteScore

0.60

自引率

0.00%

发文量

审稿时长

25 weeks

期刊介绍： Methods of Functional Analysis and Topology (MFAT), founded in 1995, is a peer-reviewed arXiv overlay journal publishing original articles and surveys on general methods and techniques of functional analysis and topology with a special emphasis on applications to modern mathematical physics.