Generalized Ordinary Differential Equations: Not Absolutely Continuous Solutions

✍ Scribed by Kurzweil, Jaroslav

Publisher: World Scientific Publishing Company
Year: 2012
Tongue: English
Leaves: 208
Category: Library

No coin nor oath required. For personal study only.

✦ Table of Contents

Contents......Page 8
Preface......Page 6
1. Introduction......Page 12
2. Kapitza’s pendulum and a related problem......Page 20
3. Elementary methods: averaging......Page 22
4. Elementary methods: internal resonance......Page 26
5. Strong Riemann-integration of functions of a pair of coupled variables......Page 38
6. Generalized ordinary differential equations: Strong Riemann-solutions (concepts)......Page 48
7. Functions ψ1, ψ2......Page 54
8. Strong Riemann-solutions of generalized differential equations: a survey......Page 58
9. Approximate solutions: boundedness......Page 62
10. Approximate solutions: a Lipschitz condition......Page 70
11. Approximate solutions: convergence......Page 74
12. Solutions......Page 80
13. Continuous dependence......Page 88
14. Strong Kurzweil Henstock-integration of functions of a pair of coupled variables......Page 94
15. Generalized differential equations: Strong Kurzweil Henstock-solutions......Page 108
16. Uniqueness......Page 112
17. Differential equations in classical form......Page 116
18. On a class of differential equations in classical form......Page 122
19. Integration and Strong Integration......Page 130
20. A class of Strong Kurzweil Henstock-integrable functions......Page 138
21. Integration by parts......Page 146
22. A variant of Gronwall inequality......Page 156
23. Existence of solutions of a class of generalized ordinary differential equations......Page 166
24. A convergence process as a source of discontinuities in the theory of differential equations......Page 176
25. A class of Strong Riemann-integrable functions......Page 188
26. On equality of two integrals......Page 196
27. A class of Generalized ordinary differential equations with a restricted right hand side......Page 198
Appendix A. Some elementary results......Page 200
Appendix B. Trifles from functional analysis......Page 202
Bibliography......Page 204
Symbols......Page 206
Subject index......Page 208

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