Generalized ordinary differential equations : not absolutely continuous solutions : [solutions of infinite variation] / Jaroslav Kurzweil.

Format:

Book

Author/Creator:

Kurzweil, Jaroslav.

Series:

Series in real analysis ; v. 11.

Series in real analysis ; v. 11

Language:

English

Subjects (All):

Differential equations.

Physical Description:

1 online resource (208 p.)

Edition:

1st ed.

Place of Publication:

Singapore : World Scientific Pub. Co., 2012.

Language Note:

English

Summary:

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.

Contents:

Contents; Preface; 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 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

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

9786613646187

9781280669255

128066925X

9789814324038

9814324035

OCLC:

794328373