Linear Stieltjes integral equations in Banach spaces. II. Operator valued solutions

summary:This paper is a continuation of \cite9. In \cite9 results concerning equations of the form x(t) = x(a) +\int_a^t \dd[A(s)]x(s) +f(t) - f(a) were presented. The Kurzweil type Stieltjes integration in the setting of \cite6 for Banach space valued functions was used. Here we consider operator valued solutions of the homogeneous problem \Phi(t) = I +\int_d^t \dd[A(s)]\Phi(s) as well as the variation-of-constants formula for the former equation