In this paper we prove uniqueness theorems for bounded variation (shortly: BV) solutions and continuous BV-solutions of the Hammerstein and the Volterra-Hammerstein integral equations. We investigate real-valued functions and functions with values in a Banach space. (2000). Primary 45G10, 45D05; Secondary 45N05.
Mathematics Subject Classification
We examine conditions which do ensure the asymptotic almost periodicity (respectively, pseudo almost periodicity) of the convolution function f * h of f with h whenever f is asymptotically almost periodic (respectively, pseudo almost periodic) and h is a (Lebesgue) measurable function satisfying some additional assumptions. Next we make extensive use of those results to investigate on the asymptotically almost periodic (respectively, pseudo almost periodic) solutions to some differential, functional, and integral equations.
In this paper, we deal with one of the basic problems of the theory of autonomous superposition operators acting in the spaces of functions of bounded variation, namely the problem concerning their continuity. We basically consider autonomous superposition operators generated by analytic functions or functions of C 1 -class. We also investigate the problem of compactness of some classical linear and nonlinear operators acting in the space of functions of bounded variation in the sense of Jordan. We apply our results to the examination of the existence and the topological properties of solutions to nonlinear equations in those spaces.
Keywords
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.