Banach-Valued Ordinary Differential Equations

Siegfried Carl () and Seppo Heikkilä ()
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Siegfried Carl: Martin-Luther-Universität Halle-Wittenberg, Institut für Mathematik
Seppo Heikkilä: University of Oulu, Department of Mathematical Sciences

Chapter 6 in Fixed Point Theory in Ordered Sets and Applications, 2011, pp 197-259 from Springer

Abstract: Abstract 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.

Keywords: Banach Space; Cauchy Problem; Erential Equation; Banach Lattice; Initial Value Problem (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/978-1-4419-7585-0_6

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