{"title":"具有L2约束的Schrödinger-Newton系统多峰解的不存在性","authors":"Qing Guo, Li-xiu Duan","doi":"10.1007/s10255-023-1086-z","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we are concerned with the the Schrödinger-Newton system with <i>L</i><sup>2</sup>-constraint. Precisely, we prove that there cannot exist multi-peak normalized solutions concentrating at <i>k</i> different critical points of <i>V</i>(<i>x</i>) under certain assumptions on asymptotic behavior of <i>V</i>(<i>x</i>) and its first derivatives near these points. Especially, the critical points of <i>V</i>(<i>x</i>) in this paper must be degenerate.</p><p>The main tools are a local Pohozaev type of identity and the blow-up analysis. Our results also show that the asymptotic behavior of concentrated points to Schrödinger-Newton problem is quite different from the classical Schrödinger equations, which is mainly caused by the nonlocal term.</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\":\"Non-existence of Multi-peak Solutions to the Schrödinger-Newton System with L2-constraint\",\"authors\":\"Qing Guo, Li-xiu Duan\",\"doi\":\"10.1007/s10255-023-1086-z\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, we are concerned with the the Schrödinger-Newton system with <i>L</i><sup>2</sup>-constraint. Precisely, we prove that there cannot exist multi-peak normalized solutions concentrating at <i>k</i> different critical points of <i>V</i>(<i>x</i>) under certain assumptions on asymptotic behavior of <i>V</i>(<i>x</i>) and its first derivatives near these points. Especially, the critical points of <i>V</i>(<i>x</i>) in this paper must be degenerate.</p><p>The main tools are a local Pohozaev type of identity and the blow-up analysis. Our results also show that the asymptotic behavior of concentrated points to Schrödinger-Newton problem is quite different from the classical Schrödinger equations, which is mainly caused by the nonlocal term.</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/s10255-023-1086-z\",\"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/s10255-023-1086-z","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Non-existence of Multi-peak Solutions to the Schrödinger-Newton System with L2-constraint
In this paper, we are concerned with the the Schrödinger-Newton system with L2-constraint. Precisely, we prove that there cannot exist multi-peak normalized solutions concentrating at k different critical points of V(x) under certain assumptions on asymptotic behavior of V(x) and its first derivatives near these points. Especially, the critical points of V(x) in this paper must be degenerate.
The main tools are a local Pohozaev type of identity and the blow-up analysis. Our results also show that the asymptotic behavior of concentrated points to Schrödinger-Newton problem is quite different from the classical Schrödinger equations, which is mainly caused by the nonlocal term.
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