Static solutions for Choquard equations with Coulomb potential and upper critical growth

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dc.contributor.authorChen, Sitongcs
dc.contributor.authorRadulescu, Vicentiucs
dc.contributor.authorShu, Muhuacs
dc.contributor.authorWei, Jiuyangcs
dc.coverage.issue2cs
dc.coverage.volume392cs
dc.date.accessioned2025-07-17T08:59:25Z
dc.date.available2025-07-17T08:59:25Z
dc.date.issued2025-06-02cs
dc.description.abstractThis paper focuses on static solutions for the following Choquard equation with zero mass and Coulomb potential (Formula presented.) where >0, 187<p6, (0,3), +3 is the upper critical exponent in the sense of the Hardy–Littlewood–Sobolev inequality, I:R3R is the Riesz potential, and 14|x| is the Coulomb potential. By carefully analyzing the intricate interplay between the power and Coulomb terms, we establish three types of variational geometries of the problem and prove the following existence results based on the behavior of p: the existence of two solutions, one being a local minimizer and the other of mountain-pass type, for an explicit range 0<<Const. when 187<p<3; the existence of a positive solution if takes some particular value when p=3; the existence of a ground state solution for all >0 when 4<p<6, and for two explicit ranges >Const. when 3<p<4 and p=4. Furthermore, we obtain a non-existence result for the case p=6. Particularly, we identify different compactness thresholds for above three cases, and introduce three types of test functions to control the corresponding minimax levels to be less than prescribed thresholds, thereby overcoming the loss of compactness arising from the nonlocal critical term. The derivation of these strict inequalities is a novel contribution and constitutes one of the noteworthy highlights of this work, which is available and new for the limiting Sobolev critical problem as 0. We believe that the underlying ideas have potential for future development and can be applied to a broader range of variational problems with critical growth.en
dc.formattextcs
dc.format.extent2081-2130cs
dc.format.mimetypeapplication/pdfcs
dc.identifier.citationMATHEMATISCHE ANNALEN. 2025, vol. 392, issue 2, p. 2081-2130.en
dc.identifier.doi10.1007/s00208-025-03143-4cs
dc.identifier.issn0025-5831cs
dc.identifier.orcid0000-0003-4615-5537cs
dc.identifier.other198006cs
dc.identifier.researcheridA-1503-2012cs
dc.identifier.scopus35608668800cs
dc.identifier.urihttps://hdl.handle.net/11012/255185
dc.language.isoencs
dc.publisherSpringer Naturecs
dc.relation.ispartofMATHEMATISCHE ANNALENcs
dc.relation.urihttps://link.springer.com/article/10.1007/s00208-025-03143-4cs
dc.rightsCreative Commons Attribution 4.0 Internationalcs
dc.rights.accessopenAccesscs
dc.rights.sherpahttp://www.sherpa.ac.uk/romeo/issn/0025-5831/cs
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/cs
dc.subjectSchrödingeren
dc.subjectexistenceen
dc.subjectSoboleven
dc.titleStatic solutions for Choquard equations with Coulomb potential and upper critical growthen
dc.type.driverarticleen
dc.type.statusPeer-revieweden
dc.type.versionpublishedVersionen
sync.item.dbidVAV-198006en
sync.item.dbtypeVAVen
sync.item.insts2025.07.17 10:59:25en
sync.item.modts2025.07.17 10:34:06en
thesis.grantorVysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií. Ústav matematikycs
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