Geodesic
On the Peano theorem in infinite-dimensional spaces
Matematičeskie zametki, Tome 11 (1972) no. 5, pp. 569-576 Cet article a éte moissonné depuis la source Math-Net.Ru

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New sufficient conditions for a first-order ordinary differential equation in an infinite Banach space to be locally solvable and for the solution to depend continuously on a parameter are obtained. The results are applied to an integrodifferential equation. 
@article{MZM_1972_11_5_a11,
     author = {M. I. Kamenskii},
     title = {On the {Peano} theorem in infinite-dimensional spaces},
     journal = {Matemati\v{c}eskie zametki},
     pages = {569--576},
     year = {1972},
     volume = {11},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1972_11_5_a11/}
}
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M. I. Kamenskii. On the Peano theorem in infinite-dimensional spaces. Matematičeskie zametki, Tome 11 (1972) no. 5, pp. 569-576. http://geodesic.mathdoc.fr/item/MZM_1972_11_5_a11/