Geodesic
Maps which are continuously differentiable in the sense of Michal and Bastiani but not of Fr\'echet
Contemporary Mathematics. Fundamental Directions, Differential and functional differential equations, Tome 63 (2017) no. 4, pp. 543-556

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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 Frćhet. The search for such examples is motivated by studies of delay differential equations with the delay variable and not necessarily bounded. 
@article{CMFD_2017_63_4_a0,
     author = {H.-O. Walther},
     title = {Maps which are continuously differentiable in the sense of {Michal} and {Bastiani} but not of {Fr\'echet}},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {543--556},
     publisher = {mathdoc},
     volume = {63},
     number = {4},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2017_63_4_a0/}
}
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H.-O. Walther. Maps which are continuously differentiable in the sense of Michal and Bastiani but not of Fr\'echet. Contemporary Mathematics. Fundamental Directions, Differential and functional differential equations, Tome 63 (2017) no. 4, pp. 543-556. http://geodesic.mathdoc.fr/item/CMFD_2017_63_4_a0/