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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...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Singapore :
World Scientific,
2012.
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| Colección: | Series in real analysis.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Preface; 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?1,?2; 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 variables15. 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 equations25. 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; Appendix A. Some elementary results; Appendix B. Trifles from functional analysis; Bibliography; Symbols; Subject index.