STABLE PERIODIC SOLUTIONS IN SCALAR PERIODIC DIFFERENTIAL DELAY EQUATIONS.
- Resource Type
- Article
- Authors
- IVANOV, ANATOLI; SHELYAG, SERGIY
- Source
- Archivum Mathematicum. 2023, Vol. 59 Issue 1, p69-76. 8p.
- Subject
- *DIFFERENTIAL forms
*DELAY differential equations
- Language
- ISSN
- 0044-8753
A class of nonlinear simple form differential delay equations with a τ-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. [ABSTRACT FROM AUTHOR]