{"title":"Nonlinear Eigenvalue Problems for (p, 2)-Equations and Laplace Equations with Perturbations","authors":"Krzysztof Bień","doi":"10.1007/s00025-024-02176-6","DOIUrl":null,"url":null,"abstract":"<p>We consider two types of nonlinear eigenvalue problems involving Laplace and <i>p</i>-Laplace operators <span>\\((p>2)\\)</span>. The main result establishes the existence of at least two nontrivial weak solutions in the case of the perturbed equation and the existence of a continuous spectrum in the case of the (<i>p</i>, 2)-equation. In both cases, variational methods play a central role in our arguments.</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":null,"pages":null},"PeriodicalIF":1.1000,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Results in Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00025-024-02176-6","RegionNum":3,"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
Abstract
We consider two types of nonlinear eigenvalue problems involving Laplace and p-Laplace operators \((p>2)\). The main result establishes the existence of at least two nontrivial weak solutions in the case of the perturbed equation and the existence of a continuous spectrum in the case of the (p, 2)-equation. In both cases, variational methods play a central role in our arguments.
期刊介绍：
Results in Mathematics (RM) publishes mainly research papers in all fields of pure and applied mathematics. In addition, it publishes summaries of any mathematical field and surveys of any mathematical subject provided they are designed to advance some recent mathematical development.
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