### Harmonic perturbations with delay of periodic separated variables differential equations

DOI: http://dx.doi.org/10.12775/TMNA.2015.046

#### Abstract

We study the structure of the set of harmonic solutions to perturbed, nonautonomous, $T$-periodic, separated variables ODEs on manifolds. The perturbing term, supposed to be $T$-periodic in time, is allowed to contain a finite delay. Our main result extends those of \cite{FS09} and \cite{spaSepVar} but it cannot be simply deduced from them: It emerges from of a combination of the techniques exposed in those two papers.

#### Keywords

Delay differential equations, periodic solutions, differential equations on manifolds, translation operator, differential-algebraic equations

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