BVφ-solutions of nonlinear integral equations

In this paper we investigate solutions of nonlinear Hammerstein and Volterra–Hammerstein integral equations in the space of functions of bounded φ-variation in the sense of Young. We prove the existence and in some cases the existence and uniqueness of local and global solutions in this class. Real-valued as well as vector-valued functions are under our consideration. The method of our proofs is based on an application of the Banach contraction principle as well as the Leray–Schauder alternative for contractions.  2003 Elsevier Inc. All rights reserved