Multiple normalized solutions for the planar Schrödinger–Poisson system with critical exponential growth

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dc.contributor.authorChen, Sitongcs
dc.contributor.authorRadulescu, Vicentiucs
dc.contributor.authorTang, Xianhuacs
dc.coverage.issue2cs
dc.coverage.volume306cs
dc.date.accessioned2024-05-13T14:45:37Z
dc.date.available2024-05-13T14:45:37Z
dc.date.issued2024-02-16cs
dc.description.abstractThe paper deals with the existence of normalized solutions for the following Schr & ouml;dinger-Poisson system with -constraint: { -Delta u+lambda u+mu(log||& lowast;u2)u=(e(u2-)1-u2)u,x is an element of R-2, integral R(2)u(2)dx=c, where mu>0,lambda is an element of R , will arise as a Lagrange multiplier and the nonlinearity enjoys critical exponential growth of Trudinger-Moser type. By specifying explicit conditions on the energy level c, we detect a geometry of local minimum and a minimax structure for the corresponding energy functional, and prove the existence of two solutions, one being a local minimizer and one of mountain-pass type. In particular, to catch a second solution of mountain-pass type, some sharp estimates of energy levels are proposed, suggesting a new threshold of compactness in the -constraint. Our study extends and complements the results of Cingolani-Jeanjean (SIAM J Math Anal 51(4): 3533-3568, 2019) dealing with the power nonlinearity a|u|p-2uin the case ofa>0andp>4, in the case of and , which seems to be the first contribution in the context of normalized solutions. Our model presents some new difficulties due to the intricate interplay between a logarithmic convolution potential and a nonlinear term of critical exponential type and requires a novel analysis and the implementation of new ideas, especially in the compactness argument. We believe that our approach will open the door to the study of other -constrained problems with critical exponential growth, and the new underlying ideas are of future development and applicability.en
dc.formattextcs
dc.format.extent1-32cs
dc.format.mimetypeapplication/pdfcs
dc.identifier.citationMATHEMATISCHE ZEITSCHRIFT. 2024, vol. 306, issue 2, p. 1-32.en
dc.identifier.doi10.1007/s00209-024-03432-9cs
dc.identifier.issn0025-5874cs
dc.identifier.orcid0000-0003-4615-5537cs
dc.identifier.other188260cs
dc.identifier.researcheridA-1503-2012cs
dc.identifier.scopus35608668800cs
dc.identifier.urihttps://hdl.handle.net/11012/245504
dc.language.isoencs
dc.publisherSpringer Naturecs
dc.relation.ispartofMATHEMATISCHE ZEITSCHRIFTcs
dc.relation.urihttps://link.springer.com/article/10.1007/s00209-024-03432-9cs
dc.rightsCreative Commons Attribution 4.0 Internationalcs
dc.rights.accessopenAccesscs
dc.rights.sherpahttp://www.sherpa.ac.uk/romeo/issn/0025-5874/cs
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/cs
dc.subjectCritical exponential growthen
dc.subjectLogarithmic convolution potentialen
dc.subjectNormalized solutionen
dc.subjectPlanar Schrödinger–Poisson systemen
dc.subjectTrudinger–Moser inequalityen
dc.titleMultiple normalized solutions for the planar Schrödinger–Poisson system with critical exponential growthen
dc.type.driverarticleen
dc.type.statusPeer-revieweden
dc.type.versionpublishedVersionen
sync.item.dbidVAV-188260en
sync.item.dbtypeVAVen
sync.item.insts2024.05.13 16:45:37en
sync.item.modts2024.05.13 16:13:33en
thesis.grantorVysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií. Ústav matematikycs
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