On nonlinear integral equations and Λ-bounded variation

Abstract

We discuss the existence or the existence and uniqueness of global and local Λ-bounded variation (ΛBV) solutions as well as continuous ΛBV-solutions of nonlinear Hammerstein and Volterra-Hammerstein integral equations formulated in terms of the Lebesgue integral. Since the space of functions of bounded variation in the sense of Jordan is a proper subspace of functions of Λ-bounded variation and for some class of functions φ, the space of functions of bounded φ-variation in the sense of Young is also a proper subspace of the space under consideration, our results extend known results in the literature.