{"title":"Parametric Anisotropic (p, q)-Neumann Problems","authors":"Zhen-hai Liu, Nikolaos S. Papageorgiou","doi":"10.1007/s10255-023-1087-y","DOIUrl":null,"url":null,"abstract":"<div><p>We consider a Neumann problem driven by a (<i>p</i>(<i>z</i>), <i>q</i>(<i>z</i>))-Laplacian (anisotropic problem) plus a parametric potential term with λ > 0 being the parameter. The reaction is superlinear but need not satisfy the Ambrosetti-Rabinowitz condition. We prove a bifurcation-type theorem describing the changes in the set of positive solutions as the parameter λ moves on </p><div><figure><div><div><picture><source><img></source></picture></div></div></figure></div><p>.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"39 4","pages":"926 - 942"},"PeriodicalIF":0.9000,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematicae Applicatae Sinica, English Series","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10255-023-1087-y","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
We consider a Neumann problem driven by a (p(z), q(z))-Laplacian (anisotropic problem) plus a parametric potential term with λ > 0 being the parameter. The reaction is superlinear but need not satisfy the Ambrosetti-Rabinowitz condition. We prove a bifurcation-type theorem describing the changes in the set of positive solutions as the parameter λ moves on
期刊介绍：
Acta Mathematicae Applicatae Sinica (English Series) is a quarterly journal established by the Chinese Mathematical Society. The journal publishes high quality research papers from all branches of applied mathematics, and particularly welcomes those from partial differential equations, computational mathematics, applied probability, mathematical finance, statistics, dynamical systems, optimization and management science.
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