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Stable periodic solutions in scalar periodic differential delay equations

Anatoli Ivanov; Sergiy Shelyag — 2023

Archivum Mathematicum

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 $T > 4 τ - d_{0}$ , for some $d_{0} > 0$ , 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...

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