Generalized Ordinary Differential Equations Not Absolutely Continuous Solutions 2nd Edition by Jaroslav Kurzweil ISBN B00G1BIP86 9789814324038

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Product details:

ISBN 10: B00G1BIP86
ISBN 13: 9789814324038
Author: Jaroslav Kurzweil

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 suitable in situations where fast oscillations occur.

Generalized Ordinary Differential Equations Not Absolutely Continuous Solutions 2nd 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 ψ1, ψ2

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

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Tags: Jaroslav Kurzweil, Generalized Ordinary, Continuous Solutions