{"title":"有界域中空间衰减非线性 L2 次临界变分问题的最小化","authors":"Bin Chen, Yongshuai Gao, Yujin Guo, Yue Wu","doi":"10.1007/s10473-024-0312-y","DOIUrl":null,"url":null,"abstract":"<p>This paper is concerned with the minimizers of <i>L</i><sup>2</sup>-subcritical constraint variational problems with spatially decaying nonlinearities in a bounded domain Ω of ℝ<sup><i>N</i></sup> (<i>N</i> ≥ 1). We prove that the problem admits minimizers for any <i>M</i> > 0. Moreover, the limiting behavior of minimizers as <i>M</i> → ∞ is also analyzed rigorously.</p>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"7 1","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2024-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Minimizers of L2-subcritical variational problems with spatially decaying nonlinearities in bounded domains\",\"authors\":\"Bin Chen, Yongshuai Gao, Yujin Guo, Yue Wu\",\"doi\":\"10.1007/s10473-024-0312-y\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>This paper is concerned with the minimizers of <i>L</i><sup>2</sup>-subcritical constraint variational problems with spatially decaying nonlinearities in a bounded domain Ω of ℝ<sup><i>N</i></sup> (<i>N</i> ≥ 1). We prove that the problem admits minimizers for any <i>M</i> > 0. Moreover, the limiting behavior of minimizers as <i>M</i> → ∞ is also analyzed rigorously.</p>\",\"PeriodicalId\":50998,\"journal\":{\"name\":\"Acta Mathematica Scientia\",\"volume\":\"7 1\",\"pages\":\"\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2024-02-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Acta Mathematica Scientia\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s10473-024-0312-y\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematica Scientia","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10473-024-0312-y","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
本文关注在ℝN（N ≥ 1）的有界域 Ω 中具有空间衰减非线性的 L2 次临界约束变分问题的最小值。我们证明了该问题在任意 M > 0 时都存在最小值。此外，我们还严格分析了最小值在 M → ∞ 时的极限行为。
Minimizers of L2-subcritical variational problems with spatially decaying nonlinearities in bounded domains
This paper is concerned with the minimizers of L2-subcritical constraint variational problems with spatially decaying nonlinearities in a bounded domain Ω of ℝN (N ≥ 1). We prove that the problem admits minimizers for any M > 0. Moreover, the limiting behavior of minimizers as M → ∞ is also analyzed rigorously.
期刊介绍：
Acta Mathematica Scientia was founded by Prof. Li Guoping (Lee Kwok Ping) in April 1981.
The aim of Acta Mathematica Scientia is to present to the specialized readers important new achievements in the areas of mathematical sciences. The journal considers for publication of original research papers in all areas related to the frontier branches of mathematics with other science and technology.
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