The Carathéodory \(D\)-conditions and their connection with the \(D\)-continuity of the Nemytskij operator
The author discusses connections between Carathéodory type conditions for a function \(f= f(t,x)\) of two variables and continuity properties of the corresponding Nemytskij operator \(F\varphi(t)= f(t,\varphi(t))\). This extends previous work by A. V. Ponosov, Yu. V. Nepomuyashchikh, and the author.
scientific article; zbMATH DE number 1175196