Existence of Resolvent for Volterra Integral Equations on Time Scales

Abstract

We introduce the concept of 'shift operators' in order to establish sufficient conditions for the existence of the resolvent for the Volterra integral equation x(t) = f(t) + integral(t)(t0)a(t, s)x(s)Delta s, t(0) is an element of T-kappa, on time scales. The paper will serve as the foundation for future research on the qualitative analysis of solutions of Volterra integral equations on time scales, using the notion of the resolvent.