Stefan Schwabik, Mathematical Institute, Academy of Sciences of the Czech Republic, Zitna 25, 115 67 Praha 1, Czech Republic, e-mail: schwabik@math.cas.cz
Abstract: 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.
Keywords: linear Stieltjes integral equations, generalized linear differential equation, equation in Banach space
Classification (MSC 1991): 34G10, 45N05
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