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dc.contributor.authorIvanov, Anatoli F.
dc.contributor.authorVerriest, Erik I.
dc.date.accessioned2014-05-13T12:00:01Z
dc.date.accessioned2016-10-05T14:13:58Z
dc.date.available2014-05-13T12:00:01Z
dc.date.available2016-10-05T14:13:58Z
dc.date.issued2014-05-13
dc.identifier.urihttp://publications.mfo.de/handle/mfo/1080
dc.descriptionResearch in Pairs 2013en_US
dc.description.abstractWe prove the existence of periodic solutions of the differential delay equation $\varepsilon\dot{x}(t) + x(t)= f(x(t-1)), \varepsilon>0$ under the assumptions that the continuous nonlinearity $f(x)$ satisfies the negative feedback condition, $x \cdot f(x) < 0, x \neq 0$, has sufficiently large derivative at zero $|f'(0)|$, and possesses an invariant interval $I \ni 0, f(I) \subseteq I$, as a dimensional map. As $\varepsilon \to 0+$ we show the convergence of the periodic solutions to a discontinuous square wave function generated by the globally attracting 2-cycle of the map $f$.en_US
dc.language.isoenen_US
dc.publisherMathematisches Forschungsinstitut Oberwolfachen_US
dc.relation.ispartofseriesOberwolfach Preprints;2014,09
dc.subjectSingular differential equations with delayen_US
dc.subjectOscillation and instabilityen_US
dc.subjectExistence of periodic solutionsen_US
dc.subjectSchauder fixed point theoremen_US
dc.subjectInterval mapsen_US
dc.subjectGlobally attracting cyclesen_US
dc.subjectAsymptotic shape of periodic solutionsen_US
dc.titleSquare wave periodic solutions of a differential delay equationen_US
dc.typePreprinten_US
dc.identifier.doi10.14760/OWP-2014-09
local.scientificprogramResearch in Pairs 2013
local.series.idOWP-2014-09
local.subject.msc34


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