This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.Ivanov, Anatoli F.Verriest, Erik I.2019-06-2820141864-7596https://doi.org/10.34657/3219https://oa.tib.eu/renate/handle/123456789/2940We prove the existence of periodic solutions of the differential delay equation εx˙(t)+x(t)=f(x(t−1)),ε>0 under the assumptions that the continuous nonlinearity f(x) satisfies the negative feedback condition, x⋅f(x)<0,x≠0, has sufficiently large derivative at zero |f′(0)|, and possesses an invariant interval I∋0,f(I)⊆I, as a dimensional map. As ε→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.application/pdfeng510Singular differential equations with delaOscillation and instabilityExistence of periodic solutionsSchauder fixed point theoremInterval mapsGlobally attracting cyclesAsymptotic shape of periodic solutionsReport