{"title":"Resonant-Superlinear Nonhomogeneous Dirichlet Problems","authors":"Zhen Hai Liu, Nikolaos S. Papageorgiou","doi":"10.1007/s10114-023-2343-z","DOIUrl":null,"url":null,"abstract":"<div><p>We consider a Dirichlet nonlinear equation driven by the (<i>p</i>, 2)-Laplacian and with a reaction having the competing effects of a parametric asymmetric superlinear term and a resonant perturbation. We show that for all small values of the parameter the problem has at least five nontrivial smooth solutions all with sign information.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematica Sinica-English Series","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10114-023-2343-z","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
Abstract
We consider a Dirichlet nonlinear equation driven by the (p, 2)-Laplacian and with a reaction having the competing effects of a parametric asymmetric superlinear term and a resonant perturbation. We show that for all small values of the parameter the problem has at least five nontrivial smooth solutions all with sign information.
期刊介绍：
Acta Mathematica Sinica, established by the Chinese Mathematical Society in 1936, is the first and the best mathematical journal in China. In 1985, Acta Mathematica Sinica is divided into English Series and Chinese Series. The English Series is a monthly journal, publishing significant research papers from all branches of pure and applied mathematics. It provides authoritative reviews of current developments in mathematical research. Contributions are invited from researchers from all over the world.
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