On the notion of derivo-periodicity
A function \(f:\mathbb{R}\rightarrow \mathbb{R}\) is said to be almost everywhere derivo-periodic if \(f'(t)=f'(t+\omega )\) for some \(\omega > 0\) and for almost all \(t\in \mathbb{R}\). The authors of this paper obtain characterizations of almost everywhere derivo-periodic functions in the case of the functions of negligible variation on a set \(S\subset \mathbb{R} \) of (Lebesgue) measure zero, respectively for the class of generalized absolutely continuous (\(ACG_*\)) functions in the restrited sense. Next the authors prove that a De Blasi-like differentiable multivalued function is derivo-periodic if and only if it is a sum of a function of a continuous (single-valued) periodic function, linear function and a bounded interval. Derivo-periodicity in terms of the Clarke subdifferentials is also discussed. The obtained results are finally applied to differential equations and inclusions.
scientific article; zbMATH DE number 2153751
scientific article