Uniform continuity of nonautonomous superposition operators in ΛBV-spaces

Abstract

Abstract In this paper we investigate the problem of uniform continuity of nonautonomous superposition operators acting between spaces of functions of bounded Λ-variation. In particular, we give the sufficient conditions for nonautonomous superposition operators to continuously map a space of functions of bounded Λ-variation into itself. The conditions cover the generators being functions of {C^{1}} -class (in view of two variables), but also allow for less regular functions, including discontinuous generators.