On nonlinear integral equations and A-bounded variation

We discuss the existence or the existence and uniqueness of global and local A-bounded variation (Lambda BV) solutions as well as continuous Lambda BV-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 Abounded variation and for some class of functions phi, the space of functions of bounded phi-variation in the sense of Young is also a proper subspace of the space under consideration, our results extend known results in the literature.