| Title:
|
Linear Stieltjes integral equations in Banach spaces. II. Operator valued solutions (English) |
| Author:
|
Schwabik, Štefan |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
125 |
| Issue:
|
4 |
| Year:
|
2000 |
| Pages:
|
431-454 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
linear Stieltjes integral equations |
| Keyword:
|
generalized linear differential equation |
| Keyword:
|
equation in Banach space |
| MSC:
|
34G10 |
| MSC:
|
45N05 |
| idZBL:
|
Zbl 0974.34057 |
| idMR:
|
MR1802292 |
| DOI:
|
10.21136/MB.2000.126273 |
| . |
| Date available:
|
2009-09-24T21:45:20Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126273 |
| . |
| Reference:
|
[1] Ju. L. Daletskij M. G. Krejn: Stability of Solutions of Differential Equations in Banach Spaces.Nauka, Moskva, 1970. (In Russian.) MR 0352638 |
| Reference:
|
[2] N. Dunford J. T Schwartz: Linear Operators I.Interscience Publishers, New York, 1958. MR 0117523 |
| Reference:
|
[3] Ch. S. Hönig: Volterra-Stieltjes Integral Equations.North-Holland Publ. Comp., Amsterdam, 1975. MR 0499969 |
| Reference:
|
[4] J. Kurzweil: Nichtabsolut konvergente Integrale.B. G. Teubner Verlagsgesellschaft, Leipzig, 1980. Zbl 0441.28001, MR 0597703 |
| Reference:
|
[5] W. Rudin: Functional Analysis.McGraw-Hill Book Company, New York, 1973. Zbl 0253.46001, MR 0365062 |
| Reference:
|
[6] Š. Schwabik: Abstract Perron-Stieltjes integral.Math. Bohem. 121 (1996), 425-447. Zbl 0879.28021, MR 1428144 |
| Reference:
|
[7] Š. Schwabik: Generalized Ordinary Differential Equations.World Scientific, Singapore, 1992. Zbl 0781.34003, MR 1200241 |
| Reference:
|
[8] Š. Schwabik M. Tvrdý O. Vejvoda: Differential and Integral Equations.Academia & Reidel, Praha & Dordrecht, 1979. MR 0542283 |
| Reference:
|
[9] Š. Schwabik: Linear Stieltjes integral equations in Banach spaces.Math. Bohem. 124 (1999), 433-457. MR 1722877 |
| . |
