Vanishing and blow-up solutions to a class of nonlinear complex differential equations near the singular point

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dc.contributor.authorDiblík, Josefcs
dc.contributor.authorRůžičková, Miroslavacs
dc.coverage.issue1cs
dc.coverage.volume13cs
dc.date.issued2024-02-05cs
dc.description.abstractA singular nonlinear differential equation z(sigma) dw/dz = aw + zwf(z , w), where sigma > 1, is considered in a neighbourhood of the point z = 0 z=0 located either in the complex plane C if sigma is a natural number, in a Riemann surface of a rational function if sigma is a rational number, or in the Riemann surface of logarithmic function if sigma is an irrational number. It is assumed that w = w ( z ) w=w\left(z) , a is an element of C { 0 } a, and that the function f f is analytic in a neighbourhood of the origin in C x C . Considering sigma to be an integer, a rational, or an irrational number, for each of the above-mentioned cases, the existence is proved of analytic solutions w = w (z ) w=w(z) in a domain that is part of a neighbourhood of the point z = 0 z=0 in C or in the Riemann surface of either a rational or a logarithmic function. Within this domain, the property lim z -> 0 w (z) = 0 is proved and an asymptotic behaviour of w (z) s established. Several examples and figures illustrate the results derived. The blow-up phenomenon is discussed as well.en
dc.formattextcs
dc.format.extent1-44cs
dc.format.mimetypeapplication/pdfcs
dc.identifier.citationAdvances in Nonlinear Analysis. 2024, vol. 13, issue 1, p. 1-44.en
dc.identifier.doi10.1515/anona-2023-0120cs
dc.identifier.issn2191-9496cs
dc.identifier.orcid0000-0001-5009-316Xcs
dc.identifier.other188249cs
dc.identifier.researcheridD-3530-2014cs
dc.identifier.scopus6701633618cs
dc.identifier.urihttp://hdl.handle.net/11012/245497
dc.language.isoencs
dc.publisherDe Gruytercs
dc.relation.ispartofAdvances in Nonlinear Analysiscs
dc.relation.urihttps://www.degruyter.com/document/doi/10.1515/anona-2023-0120/pdfcs
dc.rightsCreative Commons Attribution 4.0 Internationalcs
dc.rights.accessopenAccesscs
dc.rights.sherpahttp://www.sherpa.ac.uk/romeo/issn/2191-9496/cs
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/cs
dc.subjectanalytic solutionen
dc.subjectasymptotic behaviouren
dc.subjectblow-up phenomenonen
dc.subjectcomplex planeen
dc.subjectdifferential equationen
dc.subjectsingular pointen
dc.titleVanishing and blow-up solutions to a class of nonlinear complex differential equations near the singular pointen
dc.type.driverarticleen
dc.type.statusPeer-revieweden
dc.type.versionpublishedVersionen
sync.item.dbidVAV-188249en
sync.item.dbtypeVAVen
sync.item.insts2025.02.03 15:40:52en
sync.item.modts2025.01.17 15:37:12en
thesis.grantorVysoké učení technické v Brně. Fakulta stavební. Ústav matematiky a deskriptivní geometriecs
thesis.grantorVysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií. Ústav matematikycs
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