{"title":"Infinite transition solutions for an Allen–Cahn equation","authors":"Wen-Long Li","doi":"10.1016/j.na.2024.113572","DOIUrl":null,"url":null,"abstract":"<div><p>We give another proof of a theorem of Rabinowitz and Stredulinsky obtaining infinite transition solutions for an Allen–Cahn equation. Rabinowitz and Stredulinsky have constructed infinite transition solutions as locally minimal solutions, but it is still an interesting question to establish these solutions by other method. Our result may attract the interest of constructing solutions with the shape of locally minimal solutions of Rabinowitz and Stredulinsky for problems defined on descrete group.</p></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"245 ","pages":"Article 113572"},"PeriodicalIF":1.3000,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nonlinear Analysis-Theory Methods & Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0362546X24000919","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2024/5/20 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We give another proof of a theorem of Rabinowitz and Stredulinsky obtaining infinite transition solutions for an Allen–Cahn equation. Rabinowitz and Stredulinsky have constructed infinite transition solutions as locally minimal solutions, but it is still an interesting question to establish these solutions by other method. Our result may attract the interest of constructing solutions with the shape of locally minimal solutions of Rabinowitz and Stredulinsky for problems defined on descrete group.
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