## 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.

### MSC:

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

Zbl 0937.34047
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