Nejmeddine Chorfi , Nikolaos S. Papageorgiou , Vicenţiu D. Rădulescu
{"title":"Eigenvalue problems with unbalanced growth","authors":"Nejmeddine Chorfi , Nikolaos S. Papageorgiou , Vicenţiu D. Rădulescu","doi":"10.1016/j.aml.2025.109548","DOIUrl":null,"url":null,"abstract":"<div><div>We consider a nonlinear eigenvalue problem driven by the nonautonomous <span><math><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></math></span>-Laplacian with unbalanced growth. Using suitable Rayleigh quotients and variational tools, we show that the problem has a continuous spectrum which is an upper half line and we also show a nonexistence result for a lower half line.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"166 ","pages":"Article 109548"},"PeriodicalIF":2.9000,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics Letters","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0893965925000989","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
We consider a nonlinear eigenvalue problem driven by the nonautonomous -Laplacian with unbalanced growth. Using suitable Rayleigh quotients and variational tools, we show that the problem has a continuous spectrum which is an upper half line and we also show a nonexistence result for a lower half line.
期刊介绍:
The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.