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Linear Stieltjes integral equations in Banach spaces II; Operator valued solutions. (English) Zbl 0974.34057
Summary: This paper is a continuation of part I [Math. Bohem. 124, No. 4, 433-457 (1999; Zbl 0937.34047)], where results concerning equations of the form \[ x(t) = x(a) +\int _a^t d [A(s)]x(s) +f(t) - f(a) \] were presented. The Kurzweil-type Stieltjes integration for Banach space valued functions was used.
Here, the author considers operator-valued solutions to the homogeneous problem \[ \Phi (t) = I +\int _d^t d[A(s)]\Phi (s) \] as well as the variation-of-constants formula for the former equation.

34G10 Linear differential equations in abstract spaces
45N05 Abstract integral equations, integral equations in abstract spaces
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