an:01602828
Zbl 0974.34057
Schwabik, ??tefan
Linear Stieltjes integral equations in Banach spaces II; Operator valued solutions
EN
Math. Bohem. 125, No. 4, 431-454 (2000).
00076351
2000
j
34G10 45N05
linear Stieltjes integral equations; generalized linear differential equation; equation in Banach space
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.
Zbl 0937.34047