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STABLE PERIODIC SOLUTIONS IN SCALAR PERIODIC DIFFERENTIAL DELAY EQUATIONS

journal contribution
posted on 2023-05-03, 23:39 authored by A Ivanov, Sergiy ShelyagSergiy Shelyag
A class of nonlinear simple form differential delay equations with a T-periodic coefficient and a constant delay τ > 0 is considered. It is shown that for an arbitrary value of the period T > 4τ − d0, for some d0 > 0, there is an equation in the class such that it possesses an asymptotically stable T-period solution. The periodic solutions are constructed explicitly for the piecewise constant nonlinearities and the periodic coefficients involved, by reduction of the problem to one-dimensional maps. The periodic solutions and their stability properties are shown to persist when the nonlinearities are “smoothed” at the discontinuity points.

History

Journal

Archivum Mathematicum

Volume

59

Pagination

69-76

Location

Brno, Czech Republic

ISSN

0044-8753

eISSN

1212-5059

Language

en

Issue

1

Publisher

Masaryk University Press

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