不平衡增长双相问题带符号信息的多解

IF 0.9 3区数学 Q2 MATHEMATICS Bulletin of the London Mathematical Society Pub Date : 2024-12-20 DOI:10.1112/blms.13218

Nikolaos S. Papageorgiou, Vicenţiu D. Rădulescu, Wen Zhang

{"title":"不平衡增长双相问题带符号信息的多解","authors":"Nikolaos S. Papageorgiou, Vicenţiu D. Rădulescu, Wen Zhang","doi":"10.1112/blms.13218","DOIUrl":null,"url":null,"abstract":"We consider a double-phase Dirichlet problem with unbalanced growth and a reaction term which is <math>\n <semantics>\n <mrow>\n <mo>(</mo>\n <mi>p</mi>\n <mo>−</mo>\n <mn>1</mn>\n <mo>)</mo>\n </mrow>\n <annotation>$(p-1)$</annotation>\n </semantics></math>-sublinear and has partial interaction with the first eigenvalue of the weighted differential operator <math>\n <semantics>\n <msubsup>\n <mi>Δ</mi>\n <mi>p</mi>\n <mi>a</mi>\n </msubsup>\n <annotation>$\\Delta _{p}^{a}$</annotation>\n </semantics></math> (nonuniform nonresonance). Using the Nehari method, we show that the problem has at least three nontrivial bounded solutions, positive, negative and nodal (sign-changing). This paper extends and complements the main results in the recent paper Papageorgiou–Pudelko–Rădulescu (Math. Annalen 385 (2023) 1707–1745). ","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 2","pages":"638-656"},"PeriodicalIF":0.9000,"publicationDate":"2024-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Multiple solutions with sign information for double-phase problems with unbalanced growth\",\"authors\":\"Nikolaos S. Papageorgiou, Vicenţiu D. Rădulescu, Wen Zhang\",\"doi\":\"10.1112/blms.13218\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider a double-phase Dirichlet problem with unbalanced growth and a reaction term which is <math>\\n <semantics>\\n <mrow>\\n <mo>(</mo>\\n <mi>p</mi>\\n <mo>−</mo>\\n <mn>1</mn>\\n <mo>)</mo>\\n </mrow>\\n <annotation>$(p-1)$</annotation>\\n </semantics></math>-sublinear and has partial interaction with the first eigenvalue of the weighted differential operator <math>\\n <semantics>\\n <msubsup>\\n <mi>Δ</mi>\\n <mi>p</mi>\\n <mi>a</mi>\\n </msubsup>\\n <annotation>$\\\\Delta _{p}^{a}$</annotation>\\n </semantics></math> (nonuniform nonresonance). Using the Nehari method, we show that the problem has at least three nontrivial bounded solutions, positive, negative and nodal (sign-changing). This paper extends and complements the main results in the recent paper Papageorgiou–Pudelko–Rădulescu (Math. Annalen 385 (2023) 1707–1745). \",\"PeriodicalId\":55298,\"journal\":{\"name\":\"Bulletin of the London Mathematical Society\",\"volume\":\"57 2\",\"pages\":\"638-656\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2024-12-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Bulletin of the London Mathematical Society\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/blms.13218\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of the London Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/blms.13218","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

我们考虑了一个不平衡增长的双相Dirichlet问题，其反应项为（p−1）$ (p-1)$ -次线性并且与加权微分算子Δ pa $\Delta的第一特征值有部分相互作用_{p}^{a}$（非均匀非共振）。利用Nehari方法，我们证明了该问题至少有三个非平凡的有界解，正解、负解和节点解（变号）。本文扩展和补充了最近论文papageorgiou - pudelko - ruridulescu (Math。年鉴385(2023)1707-1745)。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Multiple solutions with sign information for double-phase problems with unbalanced growth

We consider a double-phase Dirichlet problem with unbalanced growth and a reaction term which is $(p - 1)$ -sublinear and has partial interaction with the first eigenvalue of the weighted differential operator $Δ_{p}^{a}$ (nonuniform nonresonance). Using the Nehari method, we show that the problem has at least three nontrivial bounded solutions, positive, negative and nodal (sign-changing). This paper extends and complements the main results in the recent paper Papageorgiou–Pudelko–Rădulescu (Math. Annalen 385 (2023) 1707–1745).