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linear Stieltjes integral equations; generalized linear differential equation; equation in Banach space
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.
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