In this paper, using the properties of the Henstock-Kurzweil integral and corresponding theorems, we prove the existence theorem for the equation x' = f(t,x) and inclusion x' ∈ F(t,x) in a Banach space, where f is Henstock-Kurzweil integrable and satisfies some conditions.
@article{bwmeta1.element.bwnjournal-article-div19i1-2n3bwm,
author = {Ireneusz Kubiaczyk and Aneta Sikorska},
title = {Differential equations in banach space and henstock-kurzweil integrals},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
volume = {19},
year = {1999},
pages = {35-43},
zbl = {0962.34043},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-div19i1-2n3bwm}
}
Ireneusz Kubiaczyk; Aneta Sikorska. Differential equations in banach space and henstock-kurzweil integrals. Discussiones Mathematicae, Differential Inclusions, Control and Optimization, Tome 19 (1999) pp. 35-43. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-div19i1-2n3bwm/
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