Geodesic
$C^1$-smoothness of Nemytskii operators on Sobolev-type spaces of periodic functions
Commentationes Mathematicae Universitatis Carolinae, Tome 52 (2011) no. 4, pp. 507-517.

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We consider a class of Nemytskii superposition operators that covers the nonlinear part of traveling wave models from laser dynamics, population dynamics, and chemical kinetics. Our main result is the $C^1$-continuity property of these operators over Sobolev-type spaces of periodic functions.
Classification : 46E30, 47H99
Keywords: Nemytskii operators; Sobolev-type spaces of periodic functions; $C^1$-smoothness 
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     author = {Kmit, I.},
     title = {$C^1$-smoothness of {Nemytskii} operators on {Sobolev-type} spaces of periodic functions},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {507--517},
     publisher = {mathdoc},
     volume = {52},
     number = {4},
     year = {2011},
     mrnumber = {2863995},
     zbl = {1247.47044},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2011__52_4_a3/}
}
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Kmit, I. $C^1$-smoothness of Nemytskii operators on Sobolev-type spaces of periodic functions. Commentationes Mathematicae Universitatis Carolinae, Tome 52 (2011) no. 4, pp. 507-517. http://geodesic.mathdoc.fr/item/CMUC_2011__52_4_a3/