{"title":"非自治分式 HLS 下临界 Choquard 方程归一化解的存在性、多重性和渐近行为","authors":"Jianlun Liu, Hong-Rui Sun, Ziheng Zhang","doi":"10.1007/s13540-024-00338-5","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we study a class of non-autonomous lower critical fractional Choquard equation with a pure-power nonlinear perturbation. Under some reasonable assumptions on the potential function <i>h</i>, we prove the existence and discuss asymptotic behavior of ground state solutions for our problem. Meanwhile, we also prove that the number of normalized solutions is at least the number of global maximum points of <i>h</i> when <span>\\(\\varepsilon \\)</span> is small enough.</p>","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Existence, multiplicity and asymptotic behaviour of normalized solutions to non-autonomous fractional HLS lower critical Choquard equation\",\"authors\":\"Jianlun Liu, Hong-Rui Sun, Ziheng Zhang\",\"doi\":\"10.1007/s13540-024-00338-5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this paper, we study a class of non-autonomous lower critical fractional Choquard equation with a pure-power nonlinear perturbation. Under some reasonable assumptions on the potential function <i>h</i>, we prove the existence and discuss asymptotic behavior of ground state solutions for our problem. Meanwhile, we also prove that the number of normalized solutions is at least the number of global maximum points of <i>h</i> when <span>\\\\(\\\\varepsilon \\\\)</span> is small enough.</p>\",\"PeriodicalId\":2,\"journal\":{\"name\":\"ACS Applied Bio Materials\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.6000,\"publicationDate\":\"2024-09-13\",\"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/s13540-024-00338-5\",\"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/s13540-024-00338-5","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
在本文中，我们研究了一类具有纯功率非线性扰动的非自治下临界分式乔夸特方程。在势函数 h 的一些合理假设下，我们证明了问题的基态解的存在并讨论了其渐近行为。同时，我们还证明了当\(\varepsilon \)足够小时，归一化解的数目至少是 h 的全局最大点的数目。
Existence, multiplicity and asymptotic behaviour of normalized solutions to non-autonomous fractional HLS lower critical Choquard equation
In this paper, we study a class of non-autonomous lower critical fractional Choquard equation with a pure-power nonlinear perturbation. Under some reasonable assumptions on the potential function h, we prove the existence and discuss asymptotic behavior of ground state solutions for our problem. Meanwhile, we also prove that the number of normalized solutions is at least the number of global maximum points of h when \(\varepsilon \) is small enough.
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