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January/February 2009 Order properties of spaces of non-absolutely integrable vector-valued functions and applications to differential equations
S. Carl, S. Heikkilä, Guoju Ye
Differential Integral Equations 22(1/2): 135-156 (January/February 2009).

Abstract

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.

Citation

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S. Carl. S. Heikkilä. Guoju Ye. "Order properties of spaces of non-absolutely integrable vector-valued functions and applications to differential equations." Differential Integral Equations 22 (1/2) 135 - 156, January/February 2009.

Information

Published: January/February 2009
First available in Project Euclid: 20 December 2012

zbMATH: 1240.26012
MathSciNet: MR2483016

Subjects:

Rights: Copyright © 2009 Khayyam Publishing, Inc.

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Vol.22 • No. 1/2 • January/February 2009
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