{"title":"Divergent sequence of nontrivial solutions for superlinear double phase problems","authors":"Nikolaos S. Papageorgiou, C. Vetro, F. Vetro","doi":"10.3233/asy-231830","DOIUrl":null,"url":null,"abstract":"We consider a double phase (unbalanced growth) Dirichlet problem with a Carathéodory reaction f ( z , x ) which is superlinear in x but without satisfying the AR-condition. Using the symmetric mountain pass theorem, we produce a whole sequence of distinct bounded solutions which diverge to infinity.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":1.1000,"publicationDate":"2023-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Asymptotic Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3233/asy-231830","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
We consider a double phase (unbalanced growth) Dirichlet problem with a Carathéodory reaction f ( z , x ) which is superlinear in x but without satisfying the AR-condition. Using the symmetric mountain pass theorem, we produce a whole sequence of distinct bounded solutions which diverge to infinity.
期刊介绍：
The journal Asymptotic Analysis fulfills a twofold function. It aims at publishing original mathematical results in the asymptotic theory of problems affected by the presence of small or large parameters on the one hand, and at giving specific indications of their possible applications to different fields of natural sciences on the other hand. Asymptotic Analysis thus provides mathematicians with a concentrated source of newly acquired information which they may need in the analysis of asymptotic problems.
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