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The double-power nonlinear Schrödinger equation and its generalizations: uniqueness, non-degeneracy and applications

hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorLewin, Mathieu
HAL ID: 1466
ORCID: 0000-0002-1755-0207
hal.structure.identifierInstitut de Mathématiques de Bourgogne [Dijon] [IMB]
dc.contributor.authorRota Nodari, Simona
HAL ID: 741759
ORCID: 0000-0003-4301-2901
dc.date.accessioned2021-12-07T13:24:32Z
dc.date.available2021-12-07T13:24:32Z
dc.date.issued2020
dc.identifier.issn0944-2669
dc.identifier.urihttps://basepub.dauphine.psl.eu/handle/123456789/22333
dc.language.isoenen
dc.subject.ddc515en
dc.titleThe double-power nonlinear Schrödinger equation and its generalizations: uniqueness, non-degeneracy and applications
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenIn this paper we first prove a general result about the uniqueness and non-degeneracy of positive radial solutions to equations of the form Δu+g(u)=0. Our result applies in particular to the double power non-linearity where g(u)=uq−up−μu for p>q>1 and μ>0, which we discuss with more details. In this case, the non-degeneracy of the unique solution uμ allows us to derive its behavior in the two limits μ→0 and μ→μ∗ where μ∗ is the threshold of existence. This gives the uniqueness of energy minimizers at fixed mass in certain regimes. We also make a conjecture about the variations of the L2 mass of uμ in terms of μ, which we illustrate with numerical simulations. If valid, this conjecture would imply the uniqueness of energy minimizers in all cases and also give some important information about the orbital stability of uμ.
dc.relation.isversionofjnlnameCalculus of Variations and Partial Differential Equations
dc.relation.isversionofjnlvol59
dc.relation.isversionofjnlissue197
dc.relation.isversionofjnldate2020
dc.relation.isversionofjnlpages1-53
dc.relation.isversionofdoi10.1007/s00526-020-01863-w
dc.subject.ddclabelAnalyseen
dc.relation.forthcomingnonen
dc.description.ssrncandidatenon
dc.description.halcandidatenon
dc.description.readershiprecherche
dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2023-03-27T13:33:55Z
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