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Erschienen in:
2011 | OriginalPaper | Buchkapitel
Banach-Valued Ordinary Differential Equations
verfasst von : Siegfried Carl, Seppo Heikkilä
Erschienen in: Fixed Point Theory in Ordered Sets and Applications
Verlag: Springer New York
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The main purpose of this chapter is to derive well-posedness, extremality, and comparison results for solutions of discontinuous ordinary differential equations in Banach spaces. A novel feature is that functions in considered differential equations are allowed to be Henstock–Lebesgue (HL) integrable with respect to the independent variable. HL integrability can be replaced also by Bochner integrability, although it is assumed explicitly only in the last section.