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Abstract. In this paper we investigate autonomous as well as nonautonomous superposition operators acting between spaces of functions of bounded Λ-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 Λ-variation into itself. Moreover, we prove the continuity of certain autonomous superposition operators acting between various spaces of functions of bounded Λ-variation. We also examine the existence of ΛBV -solutions as well as the topological structure of such solution sets to classical nonlinear integral equations.Mathematics Subject Classification. Primary 47H30, 26A45; Secondary 45G10, 47B34.Keywords. Aronszajn-type theorem, compact embedding, existence theorem, linear integral operator of a Fredholm-type, nonlinear Hammerstein integral equation, superposition operator, variation in the sense of Jordan, Waterman sequence, Λ-variation.

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