{"title":"Leray–Lions Equations of (p, q)-Type in the Entire Space with Unbounded Potentials","authors":"Federica Mennuni, Dimitri Mugnai","doi":"10.1007/s00032-024-00391-y","DOIUrl":null,"url":null,"abstract":"<p>In this paper we prove the existence of signed bounded solutions for a quasilinear elliptic equation in <span>\\({\\mathbb {R}}^N\\)</span> driven by a Leray–Lions operator of (<i>p</i>, <i>q</i>)–type in presence of unbounded potentials. A direct approach seems to be a hard task, and for this reason we will study approximating problems in bounded domains, whose resolutions needs refined tools from nonlinear analysis. In particular, we will use a weaker version of the classical Cerami–Palais–Smale condition together with a extension of the Weierstrass Theorem due to Candela–Palmieri, as well as a generalization of a celebrated convergence result by Boccardo–Murat–Puel.</p>","PeriodicalId":49811,"journal":{"name":"Milan Journal of Mathematics","volume":"21 1","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2024-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Milan Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00032-024-00391-y","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
In this paper we prove the existence of signed bounded solutions for a quasilinear elliptic equation in \({\mathbb {R}}^N\) driven by a Leray–Lions operator of (p, q)–type in presence of unbounded potentials. A direct approach seems to be a hard task, and for this reason we will study approximating problems in bounded domains, whose resolutions needs refined tools from nonlinear analysis. In particular, we will use a weaker version of the classical Cerami–Palais–Smale condition together with a extension of the Weierstrass Theorem due to Candela–Palmieri, as well as a generalization of a celebrated convergence result by Boccardo–Murat–Puel.
期刊介绍:
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