Geodesic
Linear Stieltjes integral equations in Banach spaces. II. Operator valued solutions
Mathematica Bohemica, Tome 125 (2000) no. 4, pp. 431-454

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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.
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.
DOI : 10.21136/MB.2000.126273
Classification : 34G10, 45N05
Keywords: linear Stieltjes integral equations; generalized linear differential equation; equation in Banach space 
Schwabik, Štefan. Linear Stieltjes integral equations in Banach spaces. II. Operator valued solutions. Mathematica Bohemica, Tome 125 (2000) no. 4, pp. 431-454. doi: 10.21136/MB.2000.126273
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