{"title":"同质群中具有临界指数的非局部半线性方程解的最优衰减","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":"{\"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}","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}
Optimal decay for solutions of nonlocal semilinear equations with critical exponent in homogeneous groups
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.
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