Henstock-Kurzweil-Pettis integral and weak topologies in nonlinear integral equations on time scales

The goal of the present work is to give an existence result for a nonlinear integral equation on time scales by considering the Banach space endowed with its weak topology. More precisely, we obtain the existence of weakly continuous solutions for an integral equation that has on the right hand side the sum of two operators, one of them continuous while the other one satisfies a partial continuity condition and some integrability (in a nonabsolute sense) assumptions. (C) 2013 Mathematical Institute Slovak Academy of Sciences