On the existence of bound and ground states for some coupled nonlinear Schrödinger-Korteweg-de Vries equations

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dc.contributor.author Colorado Heras, Eduardo
dc.date.accessioned 2021-04-08T08:44:58Z
dc.date.available 2021-04-08T08:44:58Z
dc.date.issued 2017-11-01
dc.identifier.bibliographicCitation Colorado, E. (2017). On the existence of bound and ground states for some coupled nonlinear Schrödinger–Korteweg–de Vries equations. Advances in Nonlinear Analysis, 6(4), pp. 407–426.
dc.identifier.issn 2191-9496
dc.identifier.uri http://hdl.handle.net/10016/32305
dc.description.abstract We show the existence of positive bound and ground states for a system of coupled nonlinear Schrödinger–Korteweg–de Vries equations. More precisely, we prove that there exists a positive radially symmetric ground state if either the coupling coefficient satisfies β > Λ (for an appropriate constant Λ > 0) or if β > 0 under appropriate conditions on the other parameters of the problem. We also prove that there exists a positive radially symmetric bound state if either 0 < β is sufficiently small or if 0 < β < Λ under some appropriate conditions on the parameters. These results give a classification of positive solutions as well as the multiplicity of positive solutions. Furthermore, we study systems with more general power nonlinearities and systems with more than two nonlinear Schrödinger–Korteweg–de Vries equations. Our variational approach (working on the full energy functional without the L2-mass constraint) improves many previously known results and also allows us to show new results for some range of parameters not considered in the past.
dc.format.extent 20
dc.language.iso eng
dc.publisher De Gruyter Open
dc.rights © 2017 Walter de Gruyter GmbH, Berlin/Boston
dc.rights Atribución-NoComercial-SinDerivadas 3.0 España
dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subject.other Variational methods
dc.subject.other Ground states
dc.subject.other Bound states
dc.subject.other Critical point theory
dc.subject.other Perturbation methods
dc.title On the existence of bound and ground states for some coupled nonlinear Schrödinger-Korteweg-de Vries equations
dc.type article
dc.subject.eciencia Matemáticas
dc.identifier.doi https://doi.org/10.1515/anona-2015-0181
dc.rights.accessRights openAccess
dc.relation.projectID Gobierno de España. MTM2013-44123-P
dc.type.version publishedVersion
dc.identifier.publicationfirstpage 407
dc.identifier.publicationissue 4
dc.identifier.publicationlastpage 426
dc.identifier.publicationtitle Advances in Nonlinear Analysis
dc.identifier.publicationvolume 6
dc.identifier.uxxi AR/0000019945
dc.contributor.funder Ministerio de Economía y Competitividad (España)
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