dc.contributor.author Ivanov, Anatoli F. dc.contributor.author Verriest, Erik I. dc.date.accessioned 2014-05-13T12:00:01Z dc.date.accessioned 2016-10-05T14:13:58Z dc.date.available 2014-05-13T12:00:01Z dc.date.available 2016-10-05T14:13:58Z dc.date.issued 2014-05-13 dc.identifier.uri http://publications.mfo.de/handle/mfo/1080 dc.description Research in Pairs 2013 en_US dc.description.abstract We 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.iso en en_US dc.publisher Mathematisches Forschungsinstitut Oberwolfach en_US dc.relation.ispartofseries Oberwolfach Preprints;2014,09 dc.subject Singular differential equations with delay en_US dc.subject Oscillation and instability en_US dc.subject Existence of periodic solutions en_US dc.subject Schauder fixed point theorem en_US dc.subject Interval maps en_US dc.subject Globally attracting cycles en_US dc.subject Asymptotic shape of periodic solutions en_US dc.title Square wave periodic solutions of a differential delay equation en_US dc.type Preprint en_US dc.identifier.doi 10.14760/OWP-2014-09 local.scientificprogram Research in Pairs 2013 local.series.id OWP-2014-09 local.subject.msc 34
﻿