{"title":"Normalized solutions of linear and nonlinear coupled Choquard systems with potentials","authors":"Zhenyu Guo, Wenyan Jin","doi":"10.1007/s43034-024-00348-7","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we study Choquard systems with linear and nonlinear couplings with different potentials under the <span>\\(L^2\\)</span>-constraint. We use Ekland variational principle to prove this system has a normalized radially symmetric solution for <span>\\(L^2\\)</span>-subcritical case when the dimension is greater than or equal to 2 without potentials. In addition, a positive solution with prescribed <span>\\(L^2\\)</span>-constraint under some appropriate assumptions with the potentials was obtained. The proof is based on the refined energy estimates.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.2000,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Functional Analysis","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s43034-024-00348-7","RegionNum":3,"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
Abstract
In this paper, we study Choquard systems with linear and nonlinear couplings with different potentials under the \(L^2\)-constraint. We use Ekland variational principle to prove this system has a normalized radially symmetric solution for \(L^2\)-subcritical case when the dimension is greater than or equal to 2 without potentials. In addition, a positive solution with prescribed \(L^2\)-constraint under some appropriate assumptions with the potentials was obtained. The proof is based on the refined energy estimates.
期刊介绍：
Annals of Functional Analysis is published by Birkhäuser on behalf of the Tusi Mathematical Research Group.
Ann. Funct. Anal. is a peer-reviewed electronic journal publishing papers of high standards with deep results, new ideas, profound impact, and significant implications in all areas of functional analysis and all modern related topics (e.g., operator theory). Ann. Funct. Anal. normally publishes original research papers numbering 18 or fewer pages in the journal’s style. Longer papers may be submitted to the Banach Journal of Mathematical Analysis or Advances in Operator Theory.
Ann. Funct. Anal. presents the best paper award yearly. The award in the year n is given to the best paper published in the years n-1 and n-2. The referee committee consists of selected editors of the journal.
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