Basic Topological Structures of Ordinary Differential Equations
The aim of this book is a detailed study of topological effects related to continuity of the dependence of solutions on initial values and parameters. This allows us to develop cheaply a theory which deals easily with equations having singularities and with equations with multivalued right hand side...
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| Format: | eBook |
| Language: | English |
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Dordrecht
Springer Netherlands
1998, 1998
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| Edition: | 1st ed. 1998 |
| Series: | Mathematics and Its Applications
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 1 Topological and Metric Spaces
- 2 Some Properties of Topological, Metric and Euclidean Spaces
- 3 Spaces of Mappings and Spaces of Compact Subsets
- 4 Derivation and Integration
- 5 Weak Topology on the Space L1 and Derivation of Convergent Sequences
- 6 Basic Properties of Solution Spaces
- 7 Convergent Sequences of Solution Spaces
- 8 Peano, Caratheodory and Davy Conditions
- 9 Comparison Theorem
- 10 Changes of Variables, Morphisms and Maximal Extensions
- 11 Some Methods of Investigation of Equations
- 12 Equations and Inclusions with Complicated Discontinuities in the Space Variables
- 13 Equations and Inclusions of Second Order. Cauchy Problem Theory
- 14 Equations and Inclusions of Second Order. Periodic Solutions, Dirichlet Problem
- 15 Behavior of Solutions
- 16 Two-Dimensional Systems
- References
- Notation