MATHEMATICA BOHEMICA, Vol. 125, No. 4, pp. 431-454 (2000)

Linear Stieltjes integral equations in Banach spaces II; Operator valued solutions

Stefan Schwabik

Stefan Schwabik, Mathematical Institute, Academy of Sciences of the Czech Republic, Zitna 25, 115 67 Praha 1, Czech Republic, e-mail:

Abstract: This paper is a continuation of \cite {9}. In \cite {9} 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 \cite {6} for Banach space valued functions was used. \endgraf 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 (MSC2000): 34G10, 45N05

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