Differential and Integral Equations
- Differential Integral Equations
- Volume 22, Number 1/2 (2009), 135-156.
Order properties of spaces of non-absolutely integrable vector-valued functions and applications to differential equations
We prove that if the space $Y$ of Henstock-Lebesgue integrable functions from a compact real interval to a Banach space $E$ is normed by the Alexiewicz norm and ordered by a regular cone $E_+$, then the $E_+$-valued functions of $Y$ form a regular order cone of $Y$. This property is shown to hold also when $Y$ is the space of Henstock-Kurzweil integrable functions if $E$ is weakly sequentially complete and $E_+$ is normal. As an application of the obtained results we prove existence and comparison results for least and greatest solutions of nonlocal implicit initial-value problems of discontinuous functional differential equations containing non-absolutely integrable functions.
Differential Integral Equations, Volume 22, Number 1/2 (2009), 135-156.
First available in Project Euclid: 20 December 2012
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 26A39, 28B15, 34A09, 34A36, 34G20, 34K30, 46B40, 46E40, 47H07, 47J05
Carl, S.; Heikkilä, S.; Ye, Guoju. Order properties of spaces of non-absolutely integrable vector-valued functions and applications to differential equations. Differential Integral Equations 22 (2009), no. 1/2, 135--156. https://projecteuclid.org/euclid.die/1356038558