Sihua Liang, Patrizia Pucci, Yueqiang Song, Xueqi Sun
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We first establish the concentration-compactness principle for the <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_agms-2024-0006_eq_004.png\"/> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>p</m:mi> </m:math> <jats:tex-math>p</jats:tex-math> </jats:alternatives> </jats:inline-formula>-sub-Laplacian Choquard equation on the Heisenberg group, and we then prove existence results.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On a critical Choquard-Kirchhoff p-sub-Laplacian equation in ℍ n\",\"authors\":\"Sihua Liang, Patrizia Pucci, Yueqiang Song, Xueqi Sun\",\"doi\":\"10.1515/agms-2024-0006\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This article is devoted to the study of a critical Choquard-Kirchhoff <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\" xlink:href=\\\"graphic/j_agms-2024-0006_eq_001.png\\\"/> <m:math xmlns:m=\\\"http://www.w3.org/1998/Math/MathML\\\"> <m:mi>p</m:mi> </m:math> <jats:tex-math>p</jats:tex-math> </jats:alternatives> </jats:inline-formula>-sub-Laplacian equation on the entire Heisenberg group <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\" xlink:href=\\\"graphic/j_agms-2024-0006_eq_002.png\\\"/> <m:math xmlns:m=\\\"http://www.w3.org/1998/Math/MathML\\\"> <m:msup> <m:mrow> <m:mi mathvariant=\\\"double-struck\\\">H</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> </m:mrow> </m:msup> </m:math> <jats:tex-math>{{\\\\mathbb{H}}}^{n}</jats:tex-math> </jats:alternatives> </jats:inline-formula>, where the Kirchhoff function <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\" xlink:href=\\\"graphic/j_agms-2024-0006_eq_003.png\\\"/> <m:math xmlns:m=\\\"http://www.w3.org/1998/Math/MathML\\\"> <m:mi>K</m:mi> </m:math> <jats:tex-math>K</jats:tex-math> </jats:alternatives> </jats:inline-formula> can be zero at zero, i.e., the equation can be degenerate, and involving a nonlinearity, which is critical in the sense of the Hardy-Littlewood-Sobolev inequality. We first establish the concentration-compactness principle for the <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\" xlink:href=\\\"graphic/j_agms-2024-0006_eq_004.png\\\"/> <m:math xmlns:m=\\\"http://www.w3.org/1998/Math/MathML\\\"> <m:mi>p</m:mi> </m:math> <jats:tex-math>p</jats:tex-math> </jats:alternatives> </jats:inline-formula>-sub-Laplacian Choquard equation on the Heisenberg group, and we then prove existence results.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-08-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1515/agms-2024-0006\",\"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://doi.org/10.1515/agms-2024-0006","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
本文致力于研究整个海森堡群 H n {{mathbb{H}}}^{n} 上的临界乔夸德-基尔霍夫 p p -次拉普拉斯方程。 ，其中基尔霍夫函数 K K 在零点可能为零，即方程可能是退化的，并且涉及非线性，在哈代-利特尔伍德-索博列夫不等式的意义上是临界的。我们首先建立了海森堡群上 p p-子拉普拉奇乔夸德方程的集中-紧凑性原理，然后证明了存在性结果。
On a critical Choquard-Kirchhoff p-sub-Laplacian equation in ℍ n
This article is devoted to the study of a critical Choquard-Kirchhoff pp-sub-Laplacian equation on the entire Heisenberg group Hn{{\mathbb{H}}}^{n}, where the Kirchhoff function KK can be zero at zero, i.e., the equation can be degenerate, and involving a nonlinearity, which is critical in the sense of the Hardy-Littlewood-Sobolev inequality. We first establish the concentration-compactness principle for the pp-sub-Laplacian Choquard equation on the Heisenberg group, and we then prove existence results.
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