On some nonlinear operators in -spaces

In this paper we investigate autonomous as well as nonautonomous superposition operators acting between spaces of functions of bounded -variation. A particular emphasis is put on acting conditions as well as on continuity problems for such operators. In particular, we give necessary and sufficient conditions for nonautonomous superposition operators to map a space of functions of bounded -variation into itself. Moreover, we prove the continuity of certain autonomous superposition operators acting between various spaces of functions of bounded -variation. We also examine the existence of -solutions as well as the topological structure of such solution sets to classical nonlinear integral equations.