# Linear Stieltjes integral equations in Banach spaces. II. Operator valued solutions

Mathematica Bohemica (2000)

- Volume: 125, Issue: 4, page 431-454
- ISSN: 0862-7959

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topSchwabik, Štefan. "Linear Stieltjes integral equations in Banach spaces. II. Operator valued solutions." Mathematica Bohemica 125.4 (2000): 431-454. <http://eudml.org/doc/248663>.

@article{Schwabik2000,

abstract = {This paper is a continuation of [9]. In [9] results concerning equations of the form
x(t) = x(a) +at [A(s)]x(s) +f(t) - f(a)
were presented. The Kurzweil type Stieltjes integration in the setting of [6] for Banach space valued functions was used. Here we consider operator valued solutions of the homogeneous problem
(t) = I +dt [A(s)](s)
as well as the variation-of-constants formula for the former equation.},

author = {Schwabik, Štefan},

journal = {Mathematica Bohemica},

keywords = {linear Stieltjes integral equations; generalized linear differential equation; equation in Banach space; linear Stieltjes integral equations; generalized linear differential equation; equation in Banach space},

language = {eng},

number = {4},

pages = {431-454},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Linear Stieltjes integral equations in Banach spaces. II. Operator valued solutions},

url = {http://eudml.org/doc/248663},

volume = {125},

year = {2000},

}

TY - JOUR

AU - Schwabik, Štefan

TI - Linear Stieltjes integral equations in Banach spaces. II. Operator valued solutions

JO - Mathematica Bohemica

PY - 2000

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 125

IS - 4

SP - 431

EP - 454

AB - This paper is a continuation of [9]. In [9] results concerning equations of the form
x(t) = x(a) +at [A(s)]x(s) +f(t) - f(a)
were presented. The Kurzweil type Stieltjes integration in the setting of [6] for Banach space valued functions was used. Here we consider operator valued solutions of the homogeneous problem
(t) = I +dt [A(s)](s)
as well as the variation-of-constants formula for the former equation.

LA - eng

KW - linear Stieltjes integral equations; generalized linear differential equation; equation in Banach space; linear Stieltjes integral equations; generalized linear differential equation; equation in Banach space

UR - http://eudml.org/doc/248663

ER -

## References

top- Ju. L. Daletskij M. G. Krejn, Stability of Solutions of Differential Equations in Banach Spaces, Nauka, Moskva, 1970. (In Russian.) (1970) MR0352638
- N. Dunford J. T Schwartz, Linear Operators I, Interscience Publishers, New York, 1958. (1958) MR0117523
- Ch. S. Hönig, Volterra-Stieltjes Integral Equations, North-Holland Publ. Comp., Amsterdam, 1975. (1975) MR0499969
- J. Kurzweil, Nichtabsolut konvergente Integrale, B. G. Teubner Verlagsgesellschaft, Leipzig, 1980. (1980) Zbl0441.28001MR0597703
- W. Rudin, Functional Analysis, McGraw-Hill Book Company, New York, 1973. (1973) Zbl0253.46001MR0365062
- Š. Schwabik, Abstract Perron-Stieltjes integral, Math. Bohem. 121 (1996), 425-447. (1996) Zbl0879.28021MR1428144
- Š. Schwabik, Generalized Ordinary Differential Equations, World Scientific, Singapore, 1992. (1992) Zbl0781.34003MR1200241
- Š. Schwabik M. Tvrdý O. Vejvoda, Differential and Integral Equations, Academia & Reidel, Praha & Dordrecht, 1979. (1979) MR0542283
- Š. Schwabik, Linear Stieltjes integral equations in Banach spaces, Math. Bohem. 124 (1999), 433-457. (1999) MR1722877

## Citations in EuDML Documents

top- Štefan Schwabik, Operator-valued functions of bounded semivariation and convolutions
- Štefan Schwabik, A note on integration by parts for abstract Perron-Stieltjes integrals
- Giselle A. Monteiro, Milan Tvrdý, On Kurzweil-Stieltjes integral in a Banach space
- Umi Mahnuna Hanung, Milan Tvrdý, On the relationships between Stieltjes type integrals of Young, Dushnik and Kurzweil
- Rodolfo Collegari, Márcia Federson, Miguel Frasson, Linear FDEs in the frame of generalized ODEs: variation-of-constants formula

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