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Generalized ordinary differential equations : not absolutely continuous solutions /

This book provides a systematic treatment of the Volterra integral equation by means of a modern integration theory which extends considerably the field of differential equations. It contains many new concepts and results in the framework of a unifying theory. In particular, this new approach is sui...

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Bibliographic Details
Main Author: Kurzweil, Jaroslav
Corporate Author: ebrary, Inc
Format: eBook
Language:English
Published: Singapore ; Hackensack, N.J. : World Scientific, [2012]
Series:Series in real analysis ; v. 11.
Subjects:
Differential equations.
Integral equations.
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • 1. Introduction
  • 2. Kapitza's pendulum and a related problem
  • 3. Elementary methods: averaging
  • 4. Elementary methods: internal resonance
  • 5. Strong Riemann-integration of functions of a pair of coupled variables
  • 6. Generalized ordinary differential equations: strong Riemann-solutions (concepts)
  • 7. Functions [symbol], [symbol]
  • 8. Strong Riemann-solutions of generalized differential equations: a survey
  • 9. Approximate solutions: boundedness
  • 10. Approximate solutions: a Lipschitz condition
  • 11. Approximate solutions: convergence
  • 12. Solutions
  • 13. Continuous dependence
  • 14. Strong Kurzweil Henstock-integration of functions of a pair of coupled variables
  • 15. Generalized differential equations: Strong Kurzweil Henstock-solutions
  • 16. Uniqueness
  • 17. Differential equations in classical form
  • 18. On a class of differential equations in classical form
  • 19. Integration and Strong integration
  • 20. A class of Strong Kurzweil Henstock-integrable functions
  • 21. Integration by parts
  • 22. A variant of Gronwall inequality
  • 23. Existence of solutions of a class of generalized ordinary differential equations
  • 24. A convergence process as a source of discontinuities in the theory of differential equations
  • 25. A class of Strong Riemann-integrable functions
  • 26. On equality of two integrals
  • 27. A class of generalized ordinary differential equations with a restricted right hand side.