{"title":"参数各向异性（p，q）-Neumann问题","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":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"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\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2023-11-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10255-023-1087-y\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10255-023-1087-y","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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
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