Multiplicity of solutions for a class of critical Schrödinger-Poisson systems on the Heisenberg group

We deal with multiplicity of solutions to the following Schrödinger-Poisson-type system in this article: where is the Kohn-Laplacian and is a smooth bounded region on the first Heisenberg group , , and are some real parameters, and , satisfying natural growth conditions. By the limit index theory an...

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Bibliographic Details
Published inOpen mathematics (Warsaw, Poland) Vol. 21; no. 1; pp. 262 - 279
Main Authors Li, Shiqi, Song, Yueqiang
Format Journal Article
LanguageEnglish
Published Warsaw De Gruyter 13.09.2023
De Gruyter Poland
Subjects
35J20
35R03
46E35
concentration compactness principles
Heisenberg group
limit index
Schrödinger-Poisson-type system
variational methods
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Summary:We deal with multiplicity of solutions to the following Schrödinger-Poisson-type system in this article: where is the Kohn-Laplacian and is a smooth bounded region on the first Heisenberg group , , and are some real parameters, and , satisfying natural growth conditions. By the limit index theory and the concentration compactness principles, we prove that the aforementioned system has multiplicity of solutions for , where is the best Sobolev constant. The novelties of this article are the presence of critical nonlinear term, and the system is set on the Heisenberg group.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:2391-5455
2391-5455
DOI:10.1515/math-2023-0113