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dc.contributor.authorEkeland, Ivar*
dc.contributor.authorSéré, Eric*
dc.date.accessioned2020-04-28T12:50:29Z
dc.date.available2020-04-28T12:50:29Z
dc.date.issued2020
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/20668
dc.language.isoenen
dc.subjectnonlinear Schrodinger system
dc.subjectEkeland's variational principle
dc.subjectCauchy problem
dc.subjectNash-Moser theorem
dc.subjectInverse function theorem
dc.subjectloss of derivatives
dc.subjectsingular perturbations
dc.subject.ddc510en
dc.titleA surjection theorem for maps with singular perturbation and loss of derivatives
dc.typeDocument de travail / Working paper
dc.description.abstractenIn this paper we introduce a new algorithm for solving perturbed nonlinear functional equations which admit a right-invertible linearization, but with an inverse that loses derivatives and may blow up when the perturbation parameter ϵ goes to zero. These equations are of the form Fϵ(u)=v with Fϵ(0)=0, v small and given, u small and unknown. The main difference with the by now classical Nash-Moser algorithm is that, instead of using a regularized Newton scheme, we solve a sequence of Galerkin problems thanks to a topological argument. As a consequence, in our estimates there are no quadratic terms. For problems without perturbation parameter, our results require weaker regularity assumptions on F and v than earlier ones, such as those of Hormander. For singularly perturbed functionals, we allow v to be larger than in previous works. To illustrate this, we apply our method to a nonlinear Schrodinger Cauchy problem with concentrated initial data studied by Texier-Zumbrun, and we show that our result improves significantly on theirs.
dc.publisher.cityParisen
dc.identifier.citationpages25
dc.relation.ispartofseriestitleCahier de recherche CEREMADE, Université Paris-Dauphine
dc.identifier.urlsitehttps://hal.archives-ouvertes.fr/hal-01924328
dc.subject.ddclabelMathématiquesen
dc.description.ssrncandidatenon
dc.description.halcandidatenon
dc.description.readershiprecherche
dc.description.audienceInternational
dc.date.updated2020-06-04T13:42:15Z
hal.person.labIds60*
hal.person.labIds60*


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