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Countable Families of solutions of a limit sationay semilinear fourth-order cahn-hillard-type equation I. Mountain pass and Lusternik-Schirel'man patterns in R^N

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dc.affiliation.dptoUC3M. Departamento de Matemáticases
dc.contributor.authorÁlvarez Caudevilla, Pablo
dc.contributor.authorEvans, J. D.
dc.contributor.authorGalaktionov, Victor A.
dc.contributor.funderMinisterio de Economía y Competitividad (España)es
dc.date.accessioned2021-03-25T09:42:45Z
dc.date.available2021-03-25T09:42:45Z
dc.date.issued2016-09-22
dc.description.abstractSolutions of the stationary semilinear Cahn-Hilliard-type equation (...) which are exponentially decaying at infinity, are studied. Using the mounting pass lemma allows us to determinate the existence of a radially symmetric solution. On the other hand, the application of Lusternik-Schnirel’man (L-S) category theory shows the existence of, at least, a countable family of solutions. However, through numerical methods it is shown that the whole set of solutions, even in 1D, is much wider. This suggests that, actually, there exists, at least, a countable set of countable families of solutions, in which only the first one can be obtained by the L-S min-max approach.en
dc.description.sponsorshipThe authors would like to thank the anonymous referees by their valuable suggestions, helpful comments which further improved the content and presentation of the paper. Also, this work has been partially supported by the Ministry of Economy and Competitiveness of Spain under research project MTM2012-33258. The first author has also been supported by the Ramón y Cajal project RYC-2014-15284 of the Ministry of Economy and Competitiveness.en
dc.description.statusPublicadoes
dc.format.extent25
dc.identifier.bibliographicCitationBoundary Value Problems, (2016), Articel number: 171, (25) p.en
dc.identifier.doihttps://doi.org/10.1186/s13661-016-0677-5
dc.identifier.issn1687-2762
dc.identifier.publicationfirstpage1
dc.identifier.publicationissue171
dc.identifier.publicationlastpage25
dc.identifier.publicationtitleBoundary Value Problemsen
dc.identifier.publicationvolume2016
dc.identifier.urihttps://hdl.handle.net/10016/32222
dc.identifier.uxxiAR/0000018432
dc.language.isoengen
dc.publisherSpringerOpenen
dc.relation.projectIDGobierno de España. MTM2012-33258es
dc.relation.projectIDGobierno de España. RYC-2014-15284es
dc.rights© 2016 Álvarez-Caudevilla et al. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.en
dc.rightsAtribución-NoComercial-SinDerivadas 3.0 España*
dc.rights.accessRightsopen accessen
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/*
dc.subject.ecienciaMatemáticases
dc.subject.otherStationary Cahn-Hilliard equationen
dc.subject.otherVariational settingen
dc.subject.otherNon-Unique oscillatory solutionsen
dc.subject.otherCountable family of critical pointsen
dc.titleCountable Families of solutions of a limit sationay semilinear fourth-order cahn-hillard-type equation I. Mountain pass and Lusternik-Schirel'man patterns in R^Nen
dc.typeresearch article*
dc.type.hasVersionVoR*
dspace.entity.typePublication
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