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.

Description-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.