{"title":"Optimal decay for solutions of nonlocal semilinear equations with critical exponent in homogeneous groups","authors":"Nicola Garofalo, Annunziata Loiudice, Dimiter Vassilev","doi":"10.1017/prm.2024.58","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we establish the sharp asymptotic decay of positive solutions of the Yamabe type equation <span><span><span data-mathjax-type=\"texmath\"><span>$\\mathcal {L}_s u=u^{\\frac {Q+2s}{Q-2s}}$</span></span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240513091116353-0352:S0308210524000581:S0308210524000581_inline1.png\"/></span></span> in a homogeneous Lie group, where <span><span><span data-mathjax-type=\"texmath\"><span>$\\mathcal {L}_s$</span></span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240513091116353-0352:S0308210524000581:S0308210524000581_inline2.png\"/></span></span> represents a suitable pseudodifferential operator modelled on a class of nonlocal operators arising in conformal CR geometry.</p>","PeriodicalId":54560,"journal":{"name":"Proceedings of the Royal Society of Edinburgh Section A-Mathematics","volume":"206 1","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the Royal Society of Edinburgh Section A-Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/prm.2024.58","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 establish the sharp asymptotic decay of positive solutions of the Yamabe type equation $\mathcal {L}_s u=u^{\frac {Q+2s}{Q-2s}}$ in a homogeneous Lie group, where $\mathcal {L}_s$ represents a suitable pseudodifferential operator modelled on a class of nonlocal operators arising in conformal CR geometry.
期刊介绍：
A flagship publication of The Royal Society of Edinburgh, Proceedings A is a prestigious, general mathematics journal publishing peer-reviewed papers of international standard across the whole spectrum of mathematics, but with the emphasis on applied analysis and differential equations.
An international journal, publishing six issues per year, Proceedings A has been publishing the highest-quality mathematical research since 1884. Recent issues have included a wealth of key contributors and considered research papers.
in a homogeneous Lie group, where $\mathcal {L}_s$
represents a suitable pseudodifferential operator modelled on a class of nonlocal operators arising in conformal CR geometry.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
