By variational methods, we prove existence of planar closed curves with prescribed curvature for some classes of curvature functions. The main difficulty is to obtain bounded Palais-Smale sequences. This is achieved by adding a parameter in the problem and using a version of the"monotonicity trick"introduced by M. Struwe in 1988.
通过变分法，我们证明了一些曲率函数类别中具有规定曲率的平面闭合曲线的存在性。主要困难在于如何获得有界的 Palais-Smale 序列。为此，我们在问题中添加了一个参数，并使用了 M. Struwe 于 1988 年提出的 "单调性技巧"。
{"title":"Planar closed curves with prescribed curvature","authors":"Paolo Caldiroli, Anna Capietto","doi":"10.3934/dcds.2024056","DOIUrl":"https://doi.org/10.3934/dcds.2024056","url":null,"abstract":"By variational methods, we prove existence of planar closed curves with prescribed curvature for some classes of curvature functions. The main difficulty is to obtain bounded Palais-Smale sequences. This is achieved by adding a parameter in the problem and using a version of the\"monotonicity trick\"introduced by M. Struwe in 1988.","PeriodicalId":517407,"journal":{"name":"Discrete and Continuous Dynamical Systems","volume":"13 15","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141700097","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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Jing Wang, Wan-Tong Li, Jia-Bing Wang, Fei-Ying Yang
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