Contemporary Mathematics. Fundamental DirectionsContemporary Mathematics. Fundamental DirectionsСовременная математика. Фундаментальные направления2413-36392949-0618Peoples’ Friendship University of Russia named after Patrice Lumumba (RUDN University)2239910.22363/2413-3639-2017-63-4-543-556New ResultsНовые результатыResearch ArticleMaps Which Are Continuously Differentiable in the Sense of Michal and Bastiani but not of Fre´chetОтображения, непрерывно дифференцируемые по Михалу-Бастиани, но не по ФрешеWaltherHans-OttoВальтерХ.-О.Hans-Otto.Walther@math.uni-giessen.deMathematisches Institut, Universita¨t Gießen15122017634Differential and Functional Differential EquationsДифференциальные и функционально-дифференциальные уравнения54355606122019Copyright ©; 2019, Contemporary Mathematics. Fundamental DirectionsCopyright ©; 2019, Современная математика. Фундаментальные направления2019Contemporary Mathematics. Fundamental DirectionsСовременная математика. Фундаментальные направленияhttps://journals.rudn.ru/CMFD/article/view/22399

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 Fre´chet. The search for such examples is motivated by studies of delay differential equations with the delay variable and not necessarily bounded.

Строятся примеры нелинейных отображений в функциональных пространствах, которые непрерывно дифференцируемы в смысле Михала-Бастиани, но не в смысле Фреше. Интерес к таким примерам возникает при изучении дифференциальных уравнений с запаздыванием, в которых запаздывание переменно и не обязательно ограничено.

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