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Banach-Valued Ordinary Differential Equations

In: Fixed Point Theory in Ordered Sets and Applications

Author

Listed:
  • Siegfried Carl

    (Martin-Luther-Universität Halle-Wittenberg, Institut für Mathematik)

  • Seppo Heikkilä

    (University of Oulu, Department of Mathematical Sciences)

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.

Suggested Citation

  • Siegfried Carl & Seppo Heikkilä, 2011. "Banach-Valued Ordinary Differential Equations," Springer Books, in: Fixed Point Theory in Ordered Sets and Applications, chapter 6, pages 197-259, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4419-7585-0_6
    DOI: 10.1007/978-1-4419-7585-0_6
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