Global bifurcation diagrams of positive solutions for a class of 1D superlinear indefinite problems

dc.contributor.authorFencl, Martin
dc.contributor.authorLópez-Gómez, J
dc.date.accessioned2022-02-28T11:00:27Z
dc.date.available2022-02-28T11:00:27Z
dc.date.issued2022
dc.description.abstract-translatedThis paper analyzes the structure of the set of positive solutions of a class of one-dimensional superlinear indefinite bvp’s. It is a paradigm of how mathematical analysis aids the numerical study of a problem,whereas simultaneously its numerical study confirms and illuminates the analysis. On the analytical side, we establish the fast decay of the positive solutions as λ ↓ −∞ in the region where a(x) < 0 (see (1.1)), as well as the decay of the solutions of the parabolic counterpart of the model (see (1.2)) as λ ↓ −∞on any subinterval of [0, 1] where u0 = 0, provided u0 is a subsolution of (1.1). This result provides uswith a proof of a conjecture of [26] under an additional condition of a dynamical nature. On the numerical side, this paper ascertains the global structure of the set of positive solutions on some paradigmatic prototypes whose intricate behavior is far from predictable from existing analytical results.en
dc.format36 s.cs
dc.format.mimetypeapplication/pdf
dc.identifier.citationFENCL, M. LÓPEZ-GÓMEZ, J. Global bifurcation diagrams of positive solutions for a class of 1D superlinear indefinite problems. NONLINEARITY, 2022, roč. 35, č. 3, s. 1213-1248. ISSN: 0951-7715cs
dc.identifier.document-number749512400001
dc.identifier.doi10.1088/1361-6544/ac4a88
dc.identifier.issn0951-7715
dc.identifier.obd43935020
dc.identifier.urihttp://hdl.handle.net/11025/47048
dc.language.isoenen
dc.project.IDLO1506/PUNTIS - Podpora udržitelnosti centra NTIS - Nové technologie pro informační společnostcs
dc.project.IDGA22-18261S/Nelineární úlohy s nestandardní difuzícs
dc.publisherIOP Publishingen
dc.relation.ispartofseriesNONLINEARITYen
dc.rightsPlný text není přístupný.cs
dc.rights© IOP Publishingen
dc.rights.accessclosedAccessen
dc.subject.translatedglobal bifurcation diagramsen
dc.subject.translatedpositive solutionsen
dc.subject.translatedsuperlinear indefinite problemsen
dc.titleGlobal bifurcation diagrams of positive solutions for a class of 1D superlinear indefinite problemsen
dc.typečlánekcs
dc.typearticleen
dc.type.statusPeer-revieweden
dc.type.versionpublishedVersionen

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