Abstract
We construct examples of nonlinear maps on function spaces which are continuously differentiable in the sense of Michal and Bastiani but not in the sense of Fréchet. The search for such examples is motivated by studies of delay differential equations with the delay variable and not necessarily bounded.
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Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 63, No. 4, Differential and Functional Differential Equations, 2017.
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Walther, HO. Maps That Are Continuously Differentiable in the Michal and Bastiani Sense But Not in the Fréchet Sense. J Math Sci 259, 761–774 (2021). https://doi.org/10.1007/s10958-021-05660-4
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DOI: https://doi.org/10.1007/s10958-021-05660-4