$C^1$-smoothness of Nemytskii operators on Sobolev-type spaces of periodic functions

Abstract

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.

13 pages

References in corpus (2)

• Fredholm Alternative for Periodic-Dirichlet Problems for Linear Hyperbolic Systems
• Fredholmness and Smooth Dependence for Linear Time-Periodic Hyperbolic System