STABLE PERIODIC SOLUTIONS IN SCALAR PERIODIC DIFFERENTIAL DELAY EQUATIONS

Anatoli Ivanov, Sergiy Shelyag

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish (US)
Pages (from-to)69-76
Number of pages8
JournalArchivum Mathematicum
Issue number1
DOIs
StatePublished - 2023

All Science Journal Classification (ASJC) codes

  • General Mathematics

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