{"title":"具有临界增长的哈密尔顿型系统的周期解","authors":"Yuxia Guo, Shengyu Wu, Shusen Yan","doi":"10.1007/s00526-024-02770-0","DOIUrl":null,"url":null,"abstract":"<p>We consider an elliptic system of Hamiltonian type in a strip in <span>\\({\\mathbb {R}}^N\\)</span>, satisfying the periodic boundary condition for the first <i>k</i> variables. In the superlinear case with critical growth, we prove the existence of a single bubbling solution for the system under an optimal condition on <i>k</i>. The novelty of the paper is that all the estimates needed in the proof of the existence result can be obtained once the Green’s function of the Laplacian operator in a strip with periodic boundary conditions is found.</p>","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2024-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Periodic solution for Hamiltonian type systems with critical growth\",\"authors\":\"Yuxia Guo, Shengyu Wu, Shusen Yan\",\"doi\":\"10.1007/s00526-024-02770-0\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We consider an elliptic system of Hamiltonian type in a strip in <span>\\\\({\\\\mathbb {R}}^N\\\\)</span>, satisfying the periodic boundary condition for the first <i>k</i> variables. In the superlinear case with critical growth, we prove the existence of a single bubbling solution for the system under an optimal condition on <i>k</i>. The novelty of the paper is that all the estimates needed in the proof of the existence result can be obtained once the Green’s function of the Laplacian operator in a strip with periodic boundary conditions is found.</p>\",\"PeriodicalId\":2,\"journal\":{\"name\":\"ACS Applied Bio Materials\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.6000,\"publicationDate\":\"2024-06-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACS Applied Bio Materials\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s00526-024-02770-0\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATERIALS SCIENCE, BIOMATERIALS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00526-024-02770-0","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","Score":null,"Total":0}
引用次数: 0
摘要
我们考虑了在\({\mathbb {R}}^N\) 带中的哈密顿型椭圆系统，该系统满足前 k 个变量的周期性边界条件。在临界增长的超线性情况下，我们证明了在 k 的最优条件下该系统存在一个单一的冒泡解。本文的新颖之处在于，一旦找到了具有周期性边界条件的条带中拉普拉斯算子的格林函数，就可以得到证明存在结果所需的所有估计值。
Periodic solution for Hamiltonian type systems with critical growth
We consider an elliptic system of Hamiltonian type in a strip in \({\mathbb {R}}^N\), satisfying the periodic boundary condition for the first k variables. In the superlinear case with critical growth, we prove the existence of a single bubbling solution for the system under an optimal condition on k. The novelty of the paper is that all the estimates needed in the proof of the existence result can be obtained once the Green’s function of the Laplacian operator in a strip with periodic boundary conditions is found.
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