Please use this identifier to cite or link to this item: https://doi.org/10.15480/882.4173
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dc.contributor.authorSeifert, Christian-
dc.contributor.authorTrostorff, Sascha-
dc.contributor.authorWaurick, Marcus-
dc.date.accessioned2022-02-22T13:05:34Z-
dc.date.available2022-02-22T13:05:34Z-
dc.date.issued2021-09-28-
dc.identifier.citationOperator Theory: Advances and Applications 287: 51-66 (2022-01-01)de_DE
dc.identifier.isbn978-3-030-89397-2de_DE
dc.identifier.isbn978-3-030-89396-5de_DE
dc.identifier.urihttp://hdl.handle.net/11420/11746-
dc.description.abstractIn this chapter, we discuss a first application of the time derivative operator constructed in the previous chapter. More precisely, we analyse well-posedness of ordinary differential equations and will at the same time provide a Hilbert space proof of the classical Picard–Lindelöf theorem (There are different notions for this theorem. It is also called existence and uniqueness theorem for initial value problems for ordinary differential equations as well as Cauchy–Lipschitz theorem). We shall furthermore see that the abstract theory developed here also allows for more general differential equations to be considered. In particular, we will have a look at so-called delay differential equations with finite or infinite delay; neutral differential equations are considered in the exercises section.en
dc.language.isoende_DE
dc.publisherSpringerde_DE
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/de_DE
dc.subject.ddc510: Mathematikde_DE
dc.titleOrdinary differential equationsde_DE
dc.typeinBookde_DE
dc.identifier.doi10.15480/882.4173-
dc.type.dinibookPart-
dcterms.DCMITypeText-
tuhh.identifier.urnurn:nbn:de:gbv:830-882.0173029-
tuhh.oai.showtruede_DE
tuhh.abstract.englishIn this chapter, we discuss a first application of the time derivative operator constructed in the previous chapter. More precisely, we analyse well-posedness of ordinary differential equations and will at the same time provide a Hilbert space proof of the classical Picard–Lindelöf theorem (There are different notions for this theorem. It is also called existence and uniqueness theorem for initial value problems for ordinary differential equations as well as Cauchy–Lipschitz theorem). We shall furthermore see that the abstract theory developed here also allows for more general differential equations to be considered. In particular, we will have a look at so-called delay differential equations with finite or infinite delay; neutral differential equations are considered in the exercises section.de_DE
tuhh.publisher.doi10.1007/978-3-030-89397-2_4-
tuhh.publication.instituteMathematik E-10de_DE
tuhh.identifier.doi10.15480/882.4173-
tuhh.type.opusInBuch (Kapitel / Teil einer Monographie)-
dc.type.driverbookPart-
dc.type.casraiBook Chapter-
tuhh.container.startpage51de_DE
tuhh.container.endpage66de_DE
dc.rights.nationallicensefalsede_DE
tuhh.relation.ispartofseriesOperator theoryde_DE
tuhh.relation.ispartofseriesnumber287de_DE
dc.identifier.scopus2-s2.0-85124378837de_DE
local.status.inpressfalsede_DE
local.type.versionpublishedVersionde_DE
datacite.resourceTypeBook Chapter-
datacite.resourceTypeGeneralText-
item.languageiso639-1en-
item.grantfulltextopen-
item.creatorOrcidSeifert, Christian-
item.creatorOrcidTrostorff, Sascha-
item.creatorOrcidWaurick, Marcus-
item.mappedtypeinBook-
item.tuhhseriesidOperator theory-
item.creatorGNDSeifert, Christian-
item.creatorGNDTrostorff, Sascha-
item.creatorGNDWaurick, Marcus-
item.seriesrefOperator theory;287-
item.fulltextWith Fulltext-
item.openairetypeinBook-
item.openairecristypehttp://purl.org/coar/resource_type/c_3248-
item.cerifentitytypePublications-
crisitem.author.deptMathematik E-10-
crisitem.author.deptMathematik E-10-
crisitem.author.orcid0000-0001-9182-8687-
crisitem.author.orcid0000-0003-4498-3574-
crisitem.author.parentorgStudiendekanat Elektrotechnik, Informatik und Mathematik-
crisitem.author.parentorgStudiendekanat Elektrotechnik, Informatik und Mathematik-
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